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1ST DAY REVIEWER
FILIPINO
Awiting bayan – ay kinilala bilang tulang may sukat at tugma.
Bulong – ay ginagamit bilang pagbibigay-galang o pagpapasintabi sa mga bagay o pook.
- Isang matandang katawagan sa orasyon.
Kundiman – awit ng pag-ibig.
Diona o ihiman – awit sa kasal.
Talindaw – ay inaawit habang namamangka at habang nagsasagwan.
Soliranin – naman ang awitin sa paggaod.
Oyayi o hele – ang katawagan sa awiting pangpatulog ng sanggol.
Kutangkutang – awit ng lansangan.
Kumintang – malungkot na himig.
Dalit o immo – awit ng papuri, luwalhati, kaligayahan o pasasalamat.
Tingad – awit sa pamamahinga smula sa trabaho.
Sambotani – awit sa pagtatagumpay.
Dopayinim - awit sa pagtatagumpay.
Doyalanin at Indolanin – awit panlansangan.
Tingud – awit pantahanan.
Umbay – awit panlibing.
Ombayi – isang malungkot na awit.
Omiguing – isang malambing na awit.
Antas ng wika
1. Balbal – karaniwang ginagamit sa lansangan: lespu, petmalu, gurangers (matatanda), lodi, forda.
2. Kolokyal – ginagamit sa karaniwang usapan (mixed switching o pinaghahalo ang pagsasalita or
pagsusulat ng Filipino at Ingles).
3. Lalawiganin o Diyalektal – wikang ginagamit sa isang rehiyon o isang lalawigan: sambal, ilocano,
kapampangan at marami pang iba.
4. Teknikal – ginagamit sa isang tiyak na disiplina o sitwasyon: Internet, Mouse, Chat, Savings,
Checking
5. Pampanitikan – pinakamataas na antas ng wika kabilang dito ang mga matatalinhagang salita
tulad ng: nakabibinging kayahimikan, kisap mata, mahal na tao, nagpupuyos sa galit atbp.
Mga elemento ng maikling kwento:)
 Tauhan – sila ang kumikilos upang magkabuhay ang isang kwento: nagtataglay ito ng
pisikal, spirituwal, intelektuwal, at pisyolohikal na katangian.
 Tagpuan – naglalarawan ng lugar na pinagganapan ng mahalagang pangyayari sa isang
alamat.
 Panahon – kalagayan o klima ng atmospera.
 Paksa o Tema – layunin ng pagkasulat ng kwento.
 Banghay – ito ang sunod-sunod na magkakaugnay na pangyayari.
Panimula – pagpapakilala ng mga tauhan
Saglit na kasiglahan – unti unting sinasalubong ng tauhan ang kanyang suliranin.
Tunggalian – ito ang suliranin ng kuwento.
Kasukdulan – kapana panabik na bahagi ng kuwento.
Kakalasan – tulay sa wakas.
Wakas – ito ay ang resulta o kinahinatnan ng kuwento.
Pang – uring pahambing – ang pang-uring naglalarawan o nagbibigay-katangaian sa dalawang tao,
bagay, lugar o pangyayari.
1. Magkatulad: kapwa at kapareho, sing-, kasing-, magsing-, magkasing-, at ga-, gangga.
2. Di-Magkatulad:
a).hambingang palamang – matalino kaysa, mas listo kaysa, malaki-laki kaysa.
b).hambingang pasahol – di-gasino, di-gaano, di-totoo, di-lubha.
DULA- ito ay itinatanghal sa tanghalan o entabkado.
Epiko – ang mga tauhan dito ay nagtataglay ng supernatural o di pangkaraniwang katangian
Pang-ugnay – ginagamit upang maiugnay ang mga pangyayari sa isang pagsasalaysay.
 At.
 Gayundin
 Ngunit
 Sapagkat
 Dahil sa
Denotasyon – ay ang kahulugan ng salita na literal na pagpapakahulugan
Konotasyon – ang kahulugan ng salita o pahayag kapag hindi ito tuwiran .
ang wastong paggamit ng mga pang-ugnay ay nakatutulong sa pagkakarogn pagsusunod-sunod ng mga
pangyayari.
Alam mo ba na...
Naririto ang Uri ng pang-ugnay andagdag o adisyon -Nagsasaad ito ng diwa ng pagpupuno o pagdaragdag
ng impormasyon.Halimbawa: at,pati,saka
Sa isang kubong kinatatanglawan lamang ng lampara ay nakahiga sa isang payak na higaan ang isang
payat at maputlang babae na halos hindi makakilos dahil sa malubhang sakit.
2.Pagbibigay-eksepsiyon - Nagsasad ng pagbubukod o paghihiwalay.
Halimbawa:maliban sa, bukod sa, bukod kay, puwera, huwag lang, kundi lang
Bukod sa pagputol ng kahoy na gagamitin sa pagluto, si Crispin ay nag-iigib ng tubig.
3.Pagbibigay - sanhi o dahilan- Pinag-uugnay ang mga lipon ng salita upang magbigay-katuwiran at
magsabi ng kadahilanan.
Halimbawa: dahil, sapagkat, palibhasa,kasi, mangyari, kundangan
Nagtagumpay siya dahil sa pagtitiyaga sa paggamit ng isang gaserang gaas.
4. Paglalahad ng resulta at bunga - Nagsasaad ng kinalabasan o kinahinatnan.Halimbawa: kaya, tuloy,
bunga nito, kaya naman
Sa pagdating niya sa kanilang tahanan, kaya umangat ang kabuhayan, kapuna-puna ang magandang
pagtanggap ng bawat panauhin lalo sa mga bagong mukha at siya na anak na matagal na nalayo.
5. Pagbibigay-layunin - Nagsasaad ng hangarin o naisin. Halimbawa:upang, nang sa ganon, nang sa
gayon, nang, para sa Dala ng naranasang hirap upang maging matagumpay..
6. Pagbibigay-kondisyon- Nagsasaad ng kondisyon o pasubali. Halimbawa: kapag,kung, sakali,
sandali,basta
Ang pagtatagumpay ay makakamit basta may pagtitiis, .
7.Kontrast/pagsalungat - Nagsasaad ng pag-iiba, pagkontra o pagtutol. Halimbawa:pero,ngunit, sa halip,
datapwat, subalit
Sa halip na sumuko sa hirap, magpatuloy sa pangarap.
8. Pagbibigay-kongklusyon- Nagsasaad ng panghuling pananaw o opinyon.
Halimbawa:samakatuwid, kung kaya, kaya, kung gayon, anupa't, sa wakas
Sa wakas, may pagmalasakit din ang pamahalaang lungsod.
MATH
The Scientific Notation
A number is in scientific notation if it is written as a product of a number that is greater than or equal to 1,
but less than 10, and a power of 10.
Example 1: Write 256,000 in scientific notation.
To write 256,000 in scientific notation,move the decimal point 5 places to the left to obtain a number
between 1 and 10.
The number of times the decimal point has been moved indicates the number of times 10 will be taken as a
factor.Hence, we will use 105. The exponent is positive since the decimal point was moved to the left.
Therefore, 256,000 is 2.56 x 105 in scientific notation.
Example 2: Write 0.0000000723 in scientific notation.
To write 0.0000000723 in scientific notation, move the decimal point 8 places to the right to obtain a
number between 1 and 10.
0.0000000723
The number of times the decimal point has been moved indicates the number of times 10 will be taken as a
factor. Hence, we will use10-8. The exponent is negative since the decimal point was moved to the right.
Therefore,0.0000000723 is 7.23 x 10-8 in scientific notation:
Absolute Value - of a number is the distance between that number and zero on the
number line.
Associative Property-Changing the grouping of numbers that are either being
added or multiplied does not change its value.
·Closure Property - Two integers that are added and multiplied remain as integers. The set of integers is
closed under addition and multiplication.
Commutative Property - Changing the order of two numbers that are either being
added or multiplied does not change the-value.
Distributive Property - When two numbers have been added and then multiplied by
a factor, the result will be the same when each number is
multiplied by the factor and the products are then added.
Identity Property in Addition - states that the sum of any number and 0 is the given
number. Zero (0) is the additive identity.
Identity Property in Multiplication - states that the product of any number and 1 is
the given number, a·1 = a. One (1) is the multiplicative
identity.
Integers - are whole numbers or the negative of counting numbers. The set of
integers is denoted by Z.
Z = {..., -3, -2, -1, 0, 1, 2, 3,...}.
Inverse Property In Addition - states that the sum of any number and its additive inverse is zero. The
additive inverse of the number a is -a.
Inverse Property in Multiplication - states that the product of any number and its
multiplicative inverse or reciprocal is 1.The multiplicative
inverse of the number a is
1
a
Irrational numbers - are numbers that cannot be written as a quotient of two
integers with b ≠ 0.This includes the decimals that are both
non-terminating and non-repeating. The set or irrational
numbers is denoted by Q'
Natural/Counting numbers-are the numbers we use in counting things. The set of natural numbers ,is
denoted by N. N = {1, 2, 3, 4 ...}.
Perfect square number - is a number made by squaring a whole number.
Principal n'h Root of a Number - The nth root of a number is a number whose nth power is the given
number. In symbols, if the square root of a is n=b, then b raised to the power of n.
Rational numbers - are numbers that can be written as a quotient of two integers
where b is not 0. The set of rational numbers is denoted by
Q. This set includes fractions, terminating decimals and non-terminating but repeating decimals.
Q={6/)|a,b e (Z2), b≠0}.
Real numbers - are the rational and irrational numbers. The set of real numbers is
denoted by R
R=QU
Scientific Notation - is a number written as a product of a number that is greater
than or equal to 1, but less than 10, and a power of 10.
Square root of a number - is a value that, when multiplied by itself, gives a number.
Whole numbers - are the natural or counting numbers and zero.
W={0,1W={0, 1; 2,3,4...}.
Zero Property- states that any number multiplied by zero the result is still zero.
History of Measurement
One of the earliest inventions of men was the unit of measurement. In older times, people needed
measurement to determine how long or wide things were. They needed it to build their houses, make their
clothes and prepare their food. Later, units of measurement were used in trade and commerce. In the 3rd
century BC,Egyptians used their body parts to determine measurements of things.
At first, an “inch" was the width of a man's thumb. A palm is the distance across the base of the four fingers
that form a palm. A digit is the thickness or the width of the index finger. The forearm length is called a
cubit. The handspan or “dangkal" was considered a half cubit while the palm was considered 1/6 of a cubit.
digit
cubit/forearm length
palm handspan
thumb
Go ahead, check out how many handspans there are in your forearm! The Egyptians came up with these
units to be more accurate in measuring different lengths.However,using these units of measurement had a
disadvantage. Not everyone had the same forearm length. Discrepancies arose when people started
comparing their measurements with one another because measurements of the same thing differed,
depending on who was measuring it. Hence, these units of measurement are called non-standard units of
measurement which later on evolved into what are now the inch, foot and yard. They are known as the
basic units of length in the English System of Measurement.
The English System of Measurement was widely used until the 1800s and the 1900s when the Metric
System of Measurement started to gain ground and. became the most used system of measurement
worldwide. First described by Belgian Mathematician Simon Stevin in his booklet, De Thiende (The Art of
Tenths) and proposed by English philosopher, John Wilkins, the Metric System of Measurement was first
adopted by France in 1799. In 1875,the General Conference on Weights and Measures
(Conférencegénérale des poidsetmesures or CGPM)was tasked to define the different measurements. By
1960, CGPM released the International System of Units (SI) which is now being used by majority of the
'countries with the biggest exception being the United States of America. Since our country used to be a
colony of the United States, the Filipino people were schooled in the use of the English System instead of
the Metric System of Measurement. Thus, the older generation of Filipinos is more comfortable with English
System rather than the Metric System. Moreover, the legal units of measurement in the Philippines are
based on the metric system or the SI (International System of Units) as provided for by Batas Pambansa
Bilang 8 -An Act Defining the Metric System and its Units, Providing for its Implementation and for Other
Purposes.
The Metric System of Measurement is easier to use than the English System of Measurement since its
conversion factors are consistent with the decimal system. Check out the units used in your tape mèasure.
Most likely they are inches and centimeters. The metric base unit for length is the meter, which was taken
from the Greek word metron (to measure). Units lónger or shorter than the meter are achieved by adding
prefixes to the base unit. These prefixes are also used for the base units for weight, volume, time and other
measurements. Here are the common prefixes used in the Metric System:
Metric Units of Length and Weight
describe units of measurementin the Metric
Recall that some prefixes are used to
System
Prefix,Symbol,Factor,Tera,T,x1,000,000,000,000,Giga,G,x1,000,000,000,Mega,M,x1,000,000,Kilo,k,x1,000
,Hecto,h,x100,Deka,da,x10,Deci,d,x 1/10,Centi,C,x1/100,Milli,m,x1/1,000,Micro,n,x 1/1,000,000,Nano,
n,
x1/1,000,000,000,
To convert from one unit to another, we use a conversion factor. It is a fraction composed of a numerator
and a denominator containing different units,but are referring to the same value.The conversion factor has
a value equal to one. Hence,we are not changing quantities when we multiply with it.
Example 1: Convert 3 km to m:
conversion factor: 1000 m.
1km
1
Example 2: Convert 10 mg to g:
conversion factor: 1g
1000.mg
0 mg x-1000mg=1000)9 =0.01g
Recall that volume is the amount of space an object contains or occupies. The SI unit for volume is the
cubic meter (m3). Aside from cubic meter, another commonly used metric unit for volume of solids is the
cubic centimeter (cm3 or cc) while the commonly used metric units for volume of fluids are liter (L) and
milliliter (mL). For units of volume greater or less than a liter, metric prefixes are also used. In the English
system, gallons (gal) and ounces (oz.) are used.
The table gives us some units used for measuring volume in the English System.
English System Units of Volume
gallon = 4 quarts,1 gallon = 231 cubic inches,1 quart = 2 pints,1 cubic foot = 7.48 gallons,pint = 2 cups,1
cubic yard = 200 gallons,cup = 16 tab16 tablespoons,cup = 8 flu8 fluid ounces,
The gallon is one of the most common units used in the English System. It is equal to 4 quarts or B pints.
While the cubic meter is the Sl unit for volume, the liter is also widely accepted as an sl-derived unit for
capacity. In 1964,after several revisions of its definition,the General Conference on Weights and Measures
(CGPM) finally defined a liter as equal to one cubic decimeter.Later,the'letter L was also accepted as the
symbol for liter.
The following are the units for volume in the Metric System:
1L=1dm3
1mL=1 cc or 1cm3
1000L=1m3=1 000 000 cm3
To convert from English to metric,we use: 1 gallon =3.7854 L.
We also use conversion factors (like what we did with length and weight) when we want to change one unit
of volume to another.
Example 1:Convert 5 cubic yards to gallons
5 cu. yd. x 200 gallons = 5(200)gallons =1 000 gallons
1 cubic yard 1
Example 2: Convert 12 gallons to L
12 gallon
1 gallon
Example 3:Convert 6 L to cubic inches
Honx231 cu.in.=6(1)(231) u.in.=36=366.14 cu. in. 3.7854L-L 1 gallon.7854(1)
Time
Ever since the regular movement of the sun and moon was noticed, people have wondered about the
passage of time. Today, we use the clock to measure time. The basic unit of time in the SI System is
second (s).
Currently, there are two types of notation in stating time, the 12-hr notation (standard time) and the 24-hr
notation (military or astronomical time). In military time, 1:00 PM is written as 1300 hours while 5:30 PM is
written as 1730 hours.
Here are the other units of time and.examples on how to convert from one unit to another:
1 day
1 hour
1 minute
=
=
=
24 hours(h)
60 minutes(mins)
60 seconds(s)
Examples: Convert each measure to the indicated unit.
1)4 days= h
2)12 mins= S
Solution:
1.4 days,= 4 days-x
3)5h = mins
4)45 mins= h
3.5h=_mi 5 h x 60 mins = 300m 300 mins1h
2.12
4.45 min
45
Rate and Speed
A rate is a ratio of two measurements having different units. A unit rate is a simplified rate whose
denominator is 1.
Examples:
400 words in 5 minutes is a rate
80 words in a minute is a unit rate
Speed is the rate of an object's change in position along a line. The average speed is determined by
dividing the distance travelled by the time spent to cover the distance.
Speed=distanceor S=d,read as tance per time”
Time
The SI unit for speed is meterss per second(15). The commonly used unit for
speed is kilometers per hour (kph or )for the Metric system and miles per hour
(mph or ) for the English system.
Here are some conversion factors for speed:
1km/h
1mi/h
0.2778m/s
1.4667 ft/s
= =
0.6214 mi/h
1.6093 km/h=
0.9113 ft/s
0.4470m/s
S=D/T
T=D/S
D=S×T
GLOSSARY OF TERMS
Angle-A figure formed when two rays share a common endpoint.
Digit-The thickness or the width of the index finger.
Estimate- to roughly calculate or judge the value, number or quantity.
Forearm length -distance from your elbow to the tip of your middle finger. It is also
called cubit
Handspan or “dangkal” - distance from the tip of your thumb to the tip of the litle
finger of your hand with fingers spread apart. It was considered a half
cubit.
Mass - amount of matter an object has.
Measurement - process of estimating or determining quantitative data about the
physical world, usually in relation to some standard or unit
Meter-base unit for length in the Metric System and SI. It was taken from the
Greek word metron (to measure).
Metric System Of Measurement - system of measurement based on the powers
of ten
Palm - distance across the base of the four fingers that form a palm.
Protractor-device used to measure an angle
Speed - rate of an object's change in position along a line.
Temperature - degree of hotness or coldness of án object or substance.
Thermometer - instrument used to measure temperature.
Vertex - point of intersection of rays, lines or segments
Volume - amount of space an object contains or occupies.
Weight-gravitational force acting on an object

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  • 1. 1ST DAY REVIEWER FILIPINO Awiting bayan – ay kinilala bilang tulang may sukat at tugma. Bulong – ay ginagamit bilang pagbibigay-galang o pagpapasintabi sa mga bagay o pook. - Isang matandang katawagan sa orasyon. Kundiman – awit ng pag-ibig. Diona o ihiman – awit sa kasal. Talindaw – ay inaawit habang namamangka at habang nagsasagwan. Soliranin – naman ang awitin sa paggaod. Oyayi o hele – ang katawagan sa awiting pangpatulog ng sanggol. Kutangkutang – awit ng lansangan. Kumintang – malungkot na himig. Dalit o immo – awit ng papuri, luwalhati, kaligayahan o pasasalamat. Tingad – awit sa pamamahinga smula sa trabaho. Sambotani – awit sa pagtatagumpay. Dopayinim - awit sa pagtatagumpay. Doyalanin at Indolanin – awit panlansangan. Tingud – awit pantahanan. Umbay – awit panlibing. Ombayi – isang malungkot na awit. Omiguing – isang malambing na awit.
  • 2. Antas ng wika 1. Balbal – karaniwang ginagamit sa lansangan: lespu, petmalu, gurangers (matatanda), lodi, forda. 2. Kolokyal – ginagamit sa karaniwang usapan (mixed switching o pinaghahalo ang pagsasalita or pagsusulat ng Filipino at Ingles). 3. Lalawiganin o Diyalektal – wikang ginagamit sa isang rehiyon o isang lalawigan: sambal, ilocano, kapampangan at marami pang iba. 4. Teknikal – ginagamit sa isang tiyak na disiplina o sitwasyon: Internet, Mouse, Chat, Savings, Checking 5. Pampanitikan – pinakamataas na antas ng wika kabilang dito ang mga matatalinhagang salita tulad ng: nakabibinging kayahimikan, kisap mata, mahal na tao, nagpupuyos sa galit atbp. Mga elemento ng maikling kwento:)  Tauhan – sila ang kumikilos upang magkabuhay ang isang kwento: nagtataglay ito ng pisikal, spirituwal, intelektuwal, at pisyolohikal na katangian.  Tagpuan – naglalarawan ng lugar na pinagganapan ng mahalagang pangyayari sa isang alamat.  Panahon – kalagayan o klima ng atmospera.  Paksa o Tema – layunin ng pagkasulat ng kwento.  Banghay – ito ang sunod-sunod na magkakaugnay na pangyayari. Panimula – pagpapakilala ng mga tauhan Saglit na kasiglahan – unti unting sinasalubong ng tauhan ang kanyang suliranin. Tunggalian – ito ang suliranin ng kuwento. Kasukdulan – kapana panabik na bahagi ng kuwento. Kakalasan – tulay sa wakas. Wakas – ito ay ang resulta o kinahinatnan ng kuwento. Pang – uring pahambing – ang pang-uring naglalarawan o nagbibigay-katangaian sa dalawang tao, bagay, lugar o pangyayari. 1. Magkatulad: kapwa at kapareho, sing-, kasing-, magsing-, magkasing-, at ga-, gangga. 2. Di-Magkatulad: a).hambingang palamang – matalino kaysa, mas listo kaysa, malaki-laki kaysa. b).hambingang pasahol – di-gasino, di-gaano, di-totoo, di-lubha. DULA- ito ay itinatanghal sa tanghalan o entabkado. Epiko – ang mga tauhan dito ay nagtataglay ng supernatural o di pangkaraniwang katangian
  • 3. Pang-ugnay – ginagamit upang maiugnay ang mga pangyayari sa isang pagsasalaysay.  At.  Gayundin  Ngunit  Sapagkat  Dahil sa Denotasyon – ay ang kahulugan ng salita na literal na pagpapakahulugan Konotasyon – ang kahulugan ng salita o pahayag kapag hindi ito tuwiran . ang wastong paggamit ng mga pang-ugnay ay nakatutulong sa pagkakarogn pagsusunod-sunod ng mga pangyayari. Alam mo ba na... Naririto ang Uri ng pang-ugnay andagdag o adisyon -Nagsasaad ito ng diwa ng pagpupuno o pagdaragdag ng impormasyon.Halimbawa: at,pati,saka Sa isang kubong kinatatanglawan lamang ng lampara ay nakahiga sa isang payak na higaan ang isang payat at maputlang babae na halos hindi makakilos dahil sa malubhang sakit. 2.Pagbibigay-eksepsiyon - Nagsasad ng pagbubukod o paghihiwalay. Halimbawa:maliban sa, bukod sa, bukod kay, puwera, huwag lang, kundi lang Bukod sa pagputol ng kahoy na gagamitin sa pagluto, si Crispin ay nag-iigib ng tubig. 3.Pagbibigay - sanhi o dahilan- Pinag-uugnay ang mga lipon ng salita upang magbigay-katuwiran at magsabi ng kadahilanan. Halimbawa: dahil, sapagkat, palibhasa,kasi, mangyari, kundangan Nagtagumpay siya dahil sa pagtitiyaga sa paggamit ng isang gaserang gaas. 4. Paglalahad ng resulta at bunga - Nagsasaad ng kinalabasan o kinahinatnan.Halimbawa: kaya, tuloy, bunga nito, kaya naman Sa pagdating niya sa kanilang tahanan, kaya umangat ang kabuhayan, kapuna-puna ang magandang pagtanggap ng bawat panauhin lalo sa mga bagong mukha at siya na anak na matagal na nalayo. 5. Pagbibigay-layunin - Nagsasaad ng hangarin o naisin. Halimbawa:upang, nang sa ganon, nang sa gayon, nang, para sa Dala ng naranasang hirap upang maging matagumpay.. 6. Pagbibigay-kondisyon- Nagsasaad ng kondisyon o pasubali. Halimbawa: kapag,kung, sakali, sandali,basta
  • 4. Ang pagtatagumpay ay makakamit basta may pagtitiis, . 7.Kontrast/pagsalungat - Nagsasaad ng pag-iiba, pagkontra o pagtutol. Halimbawa:pero,ngunit, sa halip, datapwat, subalit Sa halip na sumuko sa hirap, magpatuloy sa pangarap. 8. Pagbibigay-kongklusyon- Nagsasaad ng panghuling pananaw o opinyon. Halimbawa:samakatuwid, kung kaya, kaya, kung gayon, anupa't, sa wakas Sa wakas, may pagmalasakit din ang pamahalaang lungsod. MATH The Scientific Notation A number is in scientific notation if it is written as a product of a number that is greater than or equal to 1, but less than 10, and a power of 10. Example 1: Write 256,000 in scientific notation. To write 256,000 in scientific notation,move the decimal point 5 places to the left to obtain a number between 1 and 10. The number of times the decimal point has been moved indicates the number of times 10 will be taken as a factor.Hence, we will use 105. The exponent is positive since the decimal point was moved to the left. Therefore, 256,000 is 2.56 x 105 in scientific notation. Example 2: Write 0.0000000723 in scientific notation. To write 0.0000000723 in scientific notation, move the decimal point 8 places to the right to obtain a number between 1 and 10. 0.0000000723
  • 5. The number of times the decimal point has been moved indicates the number of times 10 will be taken as a factor. Hence, we will use10-8. The exponent is negative since the decimal point was moved to the right. Therefore,0.0000000723 is 7.23 x 10-8 in scientific notation: Absolute Value - of a number is the distance between that number and zero on the number line. Associative Property-Changing the grouping of numbers that are either being added or multiplied does not change its value. ·Closure Property - Two integers that are added and multiplied remain as integers. The set of integers is closed under addition and multiplication. Commutative Property - Changing the order of two numbers that are either being added or multiplied does not change the-value. Distributive Property - When two numbers have been added and then multiplied by a factor, the result will be the same when each number is multiplied by the factor and the products are then added. Identity Property in Addition - states that the sum of any number and 0 is the given number. Zero (0) is the additive identity. Identity Property in Multiplication - states that the product of any number and 1 is the given number, a·1 = a. One (1) is the multiplicative identity. Integers - are whole numbers or the negative of counting numbers. The set of integers is denoted by Z. Z = {..., -3, -2, -1, 0, 1, 2, 3,...}. Inverse Property In Addition - states that the sum of any number and its additive inverse is zero. The additive inverse of the number a is -a. Inverse Property in Multiplication - states that the product of any number and its multiplicative inverse or reciprocal is 1.The multiplicative inverse of the number a is 1
  • 6. a Irrational numbers - are numbers that cannot be written as a quotient of two integers with b ≠ 0.This includes the decimals that are both non-terminating and non-repeating. The set or irrational numbers is denoted by Q' Natural/Counting numbers-are the numbers we use in counting things. The set of natural numbers ,is denoted by N. N = {1, 2, 3, 4 ...}. Perfect square number - is a number made by squaring a whole number. Principal n'h Root of a Number - The nth root of a number is a number whose nth power is the given number. In symbols, if the square root of a is n=b, then b raised to the power of n. Rational numbers - are numbers that can be written as a quotient of two integers where b is not 0. The set of rational numbers is denoted by Q. This set includes fractions, terminating decimals and non-terminating but repeating decimals. Q={6/)|a,b e (Z2), b≠0}. Real numbers - are the rational and irrational numbers. The set of real numbers is denoted by R R=QU Scientific Notation - is a number written as a product of a number that is greater than or equal to 1, but less than 10, and a power of 10. Square root of a number - is a value that, when multiplied by itself, gives a number. Whole numbers - are the natural or counting numbers and zero. W={0,1W={0, 1; 2,3,4...}. Zero Property- states that any number multiplied by zero the result is still zero. History of Measurement One of the earliest inventions of men was the unit of measurement. In older times, people needed measurement to determine how long or wide things were. They needed it to build their houses, make their
  • 7. clothes and prepare their food. Later, units of measurement were used in trade and commerce. In the 3rd century BC,Egyptians used their body parts to determine measurements of things. At first, an “inch" was the width of a man's thumb. A palm is the distance across the base of the four fingers that form a palm. A digit is the thickness or the width of the index finger. The forearm length is called a cubit. The handspan or “dangkal" was considered a half cubit while the palm was considered 1/6 of a cubit. digit cubit/forearm length palm handspan thumb Go ahead, check out how many handspans there are in your forearm! The Egyptians came up with these units to be more accurate in measuring different lengths.However,using these units of measurement had a disadvantage. Not everyone had the same forearm length. Discrepancies arose when people started comparing their measurements with one another because measurements of the same thing differed, depending on who was measuring it. Hence, these units of measurement are called non-standard units of measurement which later on evolved into what are now the inch, foot and yard. They are known as the basic units of length in the English System of Measurement. The English System of Measurement was widely used until the 1800s and the 1900s when the Metric System of Measurement started to gain ground and. became the most used system of measurement worldwide. First described by Belgian Mathematician Simon Stevin in his booklet, De Thiende (The Art of Tenths) and proposed by English philosopher, John Wilkins, the Metric System of Measurement was first adopted by France in 1799. In 1875,the General Conference on Weights and Measures (Conférencegénérale des poidsetmesures or CGPM)was tasked to define the different measurements. By 1960, CGPM released the International System of Units (SI) which is now being used by majority of the 'countries with the biggest exception being the United States of America. Since our country used to be a colony of the United States, the Filipino people were schooled in the use of the English System instead of the Metric System of Measurement. Thus, the older generation of Filipinos is more comfortable with English System rather than the Metric System. Moreover, the legal units of measurement in the Philippines are based on the metric system or the SI (International System of Units) as provided for by Batas Pambansa Bilang 8 -An Act Defining the Metric System and its Units, Providing for its Implementation and for Other Purposes. The Metric System of Measurement is easier to use than the English System of Measurement since its conversion factors are consistent with the decimal system. Check out the units used in your tape mèasure. Most likely they are inches and centimeters. The metric base unit for length is the meter, which was taken from the Greek word metron (to measure). Units lónger or shorter than the meter are achieved by adding prefixes to the base unit. These prefixes are also used for the base units for weight, volume, time and other measurements. Here are the common prefixes used in the Metric System:
  • 8. Metric Units of Length and Weight describe units of measurementin the Metric Recall that some prefixes are used to System Prefix,Symbol,Factor,Tera,T,x1,000,000,000,000,Giga,G,x1,000,000,000,Mega,M,x1,000,000,Kilo,k,x1,000 ,Hecto,h,x100,Deka,da,x10,Deci,d,x 1/10,Centi,C,x1/100,Milli,m,x1/1,000,Micro,n,x 1/1,000,000,Nano, n, x1/1,000,000,000, To convert from one unit to another, we use a conversion factor. It is a fraction composed of a numerator and a denominator containing different units,but are referring to the same value.The conversion factor has a value equal to one. Hence,we are not changing quantities when we multiply with it. Example 1: Convert 3 km to m: conversion factor: 1000 m. 1km 1 Example 2: Convert 10 mg to g: conversion factor: 1g 1000.mg 0 mg x-1000mg=1000)9 =0.01g Recall that volume is the amount of space an object contains or occupies. The SI unit for volume is the cubic meter (m3). Aside from cubic meter, another commonly used metric unit for volume of solids is the cubic centimeter (cm3 or cc) while the commonly used metric units for volume of fluids are liter (L) and milliliter (mL). For units of volume greater or less than a liter, metric prefixes are also used. In the English system, gallons (gal) and ounces (oz.) are used. The table gives us some units used for measuring volume in the English System. English System Units of Volume gallon = 4 quarts,1 gallon = 231 cubic inches,1 quart = 2 pints,1 cubic foot = 7.48 gallons,pint = 2 cups,1 cubic yard = 200 gallons,cup = 16 tab16 tablespoons,cup = 8 flu8 fluid ounces,
  • 9. The gallon is one of the most common units used in the English System. It is equal to 4 quarts or B pints. While the cubic meter is the Sl unit for volume, the liter is also widely accepted as an sl-derived unit for capacity. In 1964,after several revisions of its definition,the General Conference on Weights and Measures (CGPM) finally defined a liter as equal to one cubic decimeter.Later,the'letter L was also accepted as the symbol for liter. The following are the units for volume in the Metric System: 1L=1dm3 1mL=1 cc or 1cm3 1000L=1m3=1 000 000 cm3 To convert from English to metric,we use: 1 gallon =3.7854 L. We also use conversion factors (like what we did with length and weight) when we want to change one unit of volume to another. Example 1:Convert 5 cubic yards to gallons 5 cu. yd. x 200 gallons = 5(200)gallons =1 000 gallons 1 cubic yard 1 Example 2: Convert 12 gallons to L 12 gallon 1 gallon Example 3:Convert 6 L to cubic inches Honx231 cu.in.=6(1)(231) u.in.=36=366.14 cu. in. 3.7854L-L 1 gallon.7854(1) Time Ever since the regular movement of the sun and moon was noticed, people have wondered about the passage of time. Today, we use the clock to measure time. The basic unit of time in the SI System is second (s). Currently, there are two types of notation in stating time, the 12-hr notation (standard time) and the 24-hr notation (military or astronomical time). In military time, 1:00 PM is written as 1300 hours while 5:30 PM is written as 1730 hours. Here are the other units of time and.examples on how to convert from one unit to another:
  • 10. 1 day 1 hour 1 minute = = = 24 hours(h) 60 minutes(mins) 60 seconds(s) Examples: Convert each measure to the indicated unit. 1)4 days= h 2)12 mins= S Solution: 1.4 days,= 4 days-x 3)5h = mins 4)45 mins= h 3.5h=_mi 5 h x 60 mins = 300m 300 mins1h 2.12 4.45 min 45 Rate and Speed A rate is a ratio of two measurements having different units. A unit rate is a simplified rate whose denominator is 1. Examples: 400 words in 5 minutes is a rate 80 words in a minute is a unit rate Speed is the rate of an object's change in position along a line. The average speed is determined by dividing the distance travelled by the time spent to cover the distance.
  • 11. Speed=distanceor S=d,read as tance per time” Time The SI unit for speed is meterss per second(15). The commonly used unit for speed is kilometers per hour (kph or )for the Metric system and miles per hour (mph or ) for the English system. Here are some conversion factors for speed: 1km/h 1mi/h 0.2778m/s 1.4667 ft/s = = 0.6214 mi/h 1.6093 km/h= 0.9113 ft/s 0.4470m/s S=D/T T=D/S D=S×T GLOSSARY OF TERMS Angle-A figure formed when two rays share a common endpoint. Digit-The thickness or the width of the index finger. Estimate- to roughly calculate or judge the value, number or quantity. Forearm length -distance from your elbow to the tip of your middle finger. It is also called cubit Handspan or “dangkal” - distance from the tip of your thumb to the tip of the litle finger of your hand with fingers spread apart. It was considered a half
  • 12. cubit. Mass - amount of matter an object has. Measurement - process of estimating or determining quantitative data about the physical world, usually in relation to some standard or unit Meter-base unit for length in the Metric System and SI. It was taken from the Greek word metron (to measure). Metric System Of Measurement - system of measurement based on the powers of ten Palm - distance across the base of the four fingers that form a palm. Protractor-device used to measure an angle Speed - rate of an object's change in position along a line. Temperature - degree of hotness or coldness of án object or substance. Thermometer - instrument used to measure temperature. Vertex - point of intersection of rays, lines or segments Volume - amount of space an object contains or occupies. Weight-gravitational force acting on an object