CONVERSION OF UNITS OF MEASUREMENTS Conversion of unit of Measurements for Length 1) Identify the unit you are starting with. 2) Identify the unit you want to end with. 3) Find the conversion factor/s that will convert the starting unit to ending unit. Using the fractional form the unit you want to end will be the numerator the unit to be cancelled will be the denominator. 4) Set up the Mathematical expression so that all units except the unit you want to end with, will not be cancelled. Convert 36 inches to feet. Solution: Step 1: inches Step 2 : feet Step 3 : (1 𝑓𝑜𝑜𝑡)/(12 𝑖𝑛𝑐ℎ𝑒𝑠) Step 4: 36 inches x (1 𝑓𝑜𝑜𝑡)/(12 𝑖𝑛𝑐ℎ𝑒𝑠) = 3 feet Step 5: Therefore, 36 in = 3 feet

2. LET’S CHECK YOUR UNDERSTANDING!
 Direction: Choose the appropriate measure.
 1. The thickness of a 25 centavo coin is _____.
 1 mm 1 cm 1 m
 2. Length of a safety pin is _____.
 26 mm 26 cm 26 m

3.  3. Long –distance run is _____.
10,000mm 10,000cm 10,000 m
 4. The weight of a can of sardines is _____.
 305 mg 305 g 305 kg
 5. The weight of a sewing needle is _____.
 380 mg 380 g 380kg

5. inches
centimeters

6. ENGLISH SYSTEM OF MEASUREMENT AND METRIC SYSTEM OF
MEASUREMENT AND ITS EQUIVALENTS
English Measurements to English
Measurements
English Measurements to Metric
Measurements
1 foot = 12 inches (in.) 1 inch = 2.54 cm
1 foot = 0.33 yards (yd.) 1 foot = 30.38 cm
1 yard = 36 in. 1 yard = 0.9 m
1 mile (mi.) = 5280 feet 1 mile = 1.6 km

7. STEPS IN THE CONVERSION OF UNITS
 1) Identify the unit you are starting with.
 2) Identify the unit you want to end with.
 3) Find the conversion factor/s that will convert the starting
unit to ending unit. Using the fractional form the unit you
want to end will be the numerator the unit to be cancelled
will be the denominator.
 4) Set up the Mathematical expression so that all units
except the unit you want to end with, will not be cancelled.

8.  Convert 36 inches to feet.
 Solution:
 Step 1: inches
 Step 2 : feet
 Step 3 :
1 𝑓𝑜𝑜𝑡
12 𝑖𝑛𝑐ℎ𝑒𝑠
 Step 4: 36 inches x
1 𝑓𝑜𝑜𝑡
12 𝑖𝑛𝑐ℎ𝑒𝑠
= 3 feet
 Step 5: Therefore, 36 in = 3 feet
EXAMPLE 1

9. Convert 2 miles in inches.
Solution:
Step 1: miles
Step 2 : inches
Step 3 :
5280 𝑓𝑒𝑒𝑡
1 𝑚𝑖𝑙𝑒
12 𝑖𝑛𝑐ℎ𝑒𝑠
1 𝑓𝑜𝑜𝑡
Step 4: 2 miles x
5280 𝑓𝑒𝑒𝑡
1 𝑚𝑖𝑙𝑒
x
12 𝑖𝑛𝑐ℎ𝑒𝑠
1 𝑓𝑜𝑜𝑡
=
2 𝑥 5280 𝑥 12 𝑖𝑛
1 𝑥 1
= 126,720 in.
Step 5: Therefore, 2 miles = 126,720 in.
EXAMPLE 2

10.  Convert 9 ft. to meters.
 Solution:
 Step 1: feet
 Step 2 : meters
 Step 3 :
0.33 𝑦𝑎𝑟𝑑𝑠
1 𝑓𝑜𝑜𝑡

0.9 𝑚
1 𝑦𝑎𝑟𝑑
 Step 4: 9 feet x
0.33 𝑦𝑎𝑟𝑑𝑠
1 𝑓𝑜𝑜𝑡
x
0.9 𝑚
1 𝑦𝑎𝑟𝑑
= 2.67 m
 Step 5: Therefore, 9 feet = 2.67 m
EXAMPLE 3

11. PREFIXES SYMBOL FACTOR Power of 10
tera T 1,000,000,000,000 1012
giga G 1,000,000,000 109
mega M 1,000,000 106
kilo K 1,000 103
hecto H 100 102
deca Da 10 101
deci D
1
10
10-1
centi C
1
100
10-2
milli M
1
1000
10-3
micro µ
1
1,000,000
10-6
nano N
1
1,000,000,000
10-9

12. CONVERSION OF UNIT OF MEASURE
Unit of Length (Meter)
10 mm = 1 cm
10 cm = 1 dm
10 dm = 1 m
10 m =1 dam
10 dkm =1 hm
10 hm =1km

14. EXAMPLE
 Convert 5.43 meters to centimeters
 In converting meter to centimeter we will move two units to the
left.
cm dm m
 So in 5.43, we will move the decimal point two places to the
right.
 Now,
 5.43 m = 5 .4 3. = 543 cm

15. EXAMPLE
 Convert 6500 meters to kilometers.
 In converting meter to kilometer we will move three units to the
right.
 m dam hm km
 So in 6500, we will move the decimal point three places to the left.
 Now,
 6500 m = 6 .5 0 0 . = 6.5 km

17.  Primitive men used to tell time by the position of the
sun, stars and the moon, and the behavior of the
animals. They used the sundial, the water clocks, and
the hourglasses for hundreds of years until the
invention of the mechanical clocks, the stately
grandfather clocks, the quartz, and digital watches,
and more recently, the atomic clocks.

18. Every girl’s most awaited celebration is their
18th birthday. Have you noticed that some
girls would tag their 18th birthday as a
decade and 8? How many years do you
think are there in a decade?

19.  In measuring time, second(s) is considered as the standard
unit. Clocks and calendars are tools for indicating time. The
two commonly used clocks are the 12-hour and the 24-hour
clocks. The 12-hour clock uses A.M. and P.M. to indicate
hours before and after noon. The A.M. is an abbreviation of
the Latin word ante meridiem means “before midday” and
P.M. is an abbreviation of the Latin word post meridiem
means “after midday”.

20. Unit Measure of Time and Their Equivalents
1 minute (min) = 60 seconds (s)
1 hour (hr) = 60 min.
1 day (d) = 24 hr
1 week (wk) = 7 d
1 month (mo) = 30 d
1 year (yr) = 12 mo = 365 d = 52 wk
1 leap year = 366 d
1 decade = 10 yr
1 score = 20 yr
1 century = 100 yr
1 millenium (pl. millenia) = 1 000 yr

21. EXAMPLES
 Alma left at 5:00 A.M. and got home at 9:00 P.M. How long
was it since she left home?
 Solution:
 21 00
 - 05 00
 16 00
 The two-time measures are just within a single day. So you can
rewrite these times as 24- hour clock: 5:00 A.M. as 5:00, and 9:00
P.M. as 21:00. Subtract the two-time measures like this:
 Therefore, Alma left home 16 hours ago.

22.  Dean can travel 4 km in 2 hours using his bicycle. What is his average
speed?
 Solution:
 Average speed refers to the distance traveled at the given time.
 Average speed =
4 𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟𝑠
2 ℎ𝑜𝑢𝑟𝑠
= 2 𝑘𝑝ℎ
 Therefore, Dean’s average speed is 2 kph.

24. VOLUME
 Volume is the amount of space occupied by an
object. The common metric units of volume are
cubic centimeters (cm3) and cubic meter (m3).
These units are obtained as the product of the
objects’ length, width and height (length x width x
height). On the other hand, Capacity is the amount
of substance a container can hold.

25. HERE ARE SOME OBJECTS THAT ILLUSTRATE THE UNITS
OF VOLUME AND CAPACITY IN THE METRIC SYSTEM.
A standard
Rubik’s cube
measures 5.7 cm
on each side.
A medicine capsule
weighs
200 milligrams.
One liter
of soft drink
.

26. LITER
Liter (L) is the basic Metric Unit for
measuring capacity. When we talk about
how much liquid or objects in a cup, a water
jug, and a basket can hold, we are referring
to the capacity of the cup, water jug and
basket as containers.

27. COMMON METRIC UNIT OF CAPACITY
Unit Relation to Liter
Kiloliter (kL) 1000 L
Hectoliter (hL) 100 L
Dekaliter (daL) 10 L
Liter (L) 1 L
Deciliter(dL) 0.1 L
Centiliter (cL) 0.01 L
Milliliter (mL) 0.001 L

28. EXAMPLES
An average household pail can hold up to
10 liters of water.
One glass of drinking water is about 240
mL.
The size of a surgical facemask box is 13
cm x 9 cm x 13 cm or 1, 521 cm3.

29. GROUP 1
 Choose whether mL or L should be used in finding
the appropriate unit of capacity.
 1. A water tank can hold up to 650 _____.
 2. One sachet of shampoo contains 12 _____.
 3. Joana buys a bottle of 500 _____ vinegar.
 4. John buys 4 _____ of gasoline.
 5. Darelyn drinks a glass of 150 _____ milk.
 6. Marie buys 1 _____ of softdrinks.

30. GROUP 2
 Choose whether cm3 or m3 should be used in finding the
appropriate unit of volume.
 1. A school backpack must have a volume of 20,000
_____.
 2. The standard size of a swimming pool is 2, 000 _____.
 3. A flash drive measures 10 _____.
 4. A ream of a long sized bondpaper is 1,123 _____.
 5. A small battery measures 8 _____.
 6. The volume of a fish pond is 80,000 ______.

31. GROUP 3
 Fill in the blank. .
 1. The ____________ system is the most common system of
measurement used in the world today.
 2. The basic unit of length in the metric system is ____________.
 3. ____________ is a unit of measure for length used for long
distances.
 4. The basic unit of measurement for weight is ______________.
 5. __________ refers to the mass subjected to gravitational
attraction.
 6. The basic unit of measurement for capacity is ____________.

32. ASSIGNMENT
 List 3 objects you see at home and measure
their length.
 List another 3 objects and measure their
weight using an appropriate unit of
measurement.
 Record your answers in the table.

33. COMPLETE THE TABLE BELOW
Name of Object Length Name of Object Weight
1. cabinet 150 cm 1. brown sugar 500 grams
2. 2.
3. 3.
4. 4.

34. EVALUATION
 Choose the letter of the best answer.
 1. What is the Greek word that was used to
come up with the English word meter?
 A. meteoron C. metronon
 B. metron D. trigonon

35. 2. Which of the following instruments used
to measure weight?
 A. beam balance C. ruler
 B. meter stick D. tape measure

36. 3. Which of the following is not a standard
unit of measure?
 A. dangkal C. liters
 B. gram D. meter

37. 4. Which of the following units has a more
precise measure in getting the measure of
the thickness of a wood?
 A. 5 km C. 5 cm
 B. 5 m D. 5 mm

38. 5. What is the volume of a pocket
dictionary?
 A. 252 mm3 C. 252 m3
 B. 252 cm3 D. 252 km3

39. 6. Which of the following units is an
appropriate unit in measuring volume or
capacity?
 A. centimeter C. kilometer
 B. cubic meter D. meter

40. 7. Which of the following devices will you
use to measure a cloth?
 A. graduated cylinder C. ruler
 B. measuring cup D. tape measure

41. 8. Rosario bought 1.3 kg of Bangus fish
while Katherine bought 1 200 grams of
Galunggong fish. Who of the two bought
more?
 A. Katherine C. both are equal
 B. Rosario D. none of them

42. 9. Mayet prepared a chocolate mixture of
about 2 000 grams to make chocolate
bars. If a chocolate bar contains 5 grams
of the chocolate mixture, how many bars
of chocolate can she prepare?
 A. 40 bars C. 4 000 bars
 B. 400 bars D. 40 000 bars

43. 10. What is the weight of a medicine
tablet?
 A. 100 t C. 100 g
 B. 100 kg D. 100 mg

44. 11. What is the weight of a ship?
 A. 200 000 t C. 200 000 g
 B. 200 000 kg D. 200 000 mg

45. 12. Jamie has to drink 0.5 L of milk every
day. How many liters of milk will she drink
in a week?
 A. 2. 5 L C. 3.5 L
 B. 3 L D. 4 L

46. 13. What is the basic unit of weight in the
metric system of measurement?
 A. gram C. milligram
 B. kilogram D. ton

47. 14. It is the amount of space occupied by
an object.
 A. area C. mass
 B. capacity D. volume

48. 15. What is the basic unit of capacity?
 A. cubic meter C. liter
 B. gram D. meter
