The document discusses measurement units and systems. It defines accuracy as how closely a measured value agrees with the correct value, and precision as how closely individual measurements agree. The metric and English systems are described. The metric system uses prefixes like kilo- and units like meters. Conversions within and between systems use conversion ratios written as fractions equal to one, allowing cancellation of units. Examples show converting between km, m, and other units.

1. MEASUREMENT

2. MEASUREMENT
•The process of getting the actual measure of an
object's dimension or property by comparing
with something that has been accepted as a
standard unit.

3. ACCURACY
•refers to how closely a measured value agrees
with the correct value.

4. PRECISION
•refers to how closely individual measurements
agree with one another. Ideally, measurements
should be both accurate and precise.

5. ACCURACY VS PRECISION

6. •Measurements may be quite precise yet
quite inaccurate because of some
systematic error, which is an error
repeated in each measurement.

7. SYSTEMS OF MEASUREMENT
•Metric System - is accepted worldwide
which was originally described as MKS
System (meter - Kilogram-second) and
later reorganized to SI or System
Internationale in 1960.

8. THE SEVEN SI BASE UNITS, WHICH ARE
COMPRISED OF:
• Length - meter (m)
• Time - second (s)
• Amount of substance - mole (mole)
• Electric current - ampere (A)
• Temperature - kelvin (K)
• Luminous intensity - candela (cd)
• Mass - kilogram (kg)

9. METRIC PREFIXES
Factor Name Symbol Multiplying Factor
1024 yotta Y
1 000 000 000 000 000
000 000 000
1021 zetta Z
1 000 000 000 000 000
000 000
1018 exa E
1 000 000 000 000 000
000
1015 peta P 1 000 000 000 000 000
1012 tera T 1 000 000 000 000
109 giga G 1 000 000 000
106 mega M 1 000 000
103 kilo k 1 000
102 hecto h 100
101 deca da 10

10. 10–1 deci d 0.1
10–2 centi c 0.01
10–3 milli m 0.001
10–6 micro µ 0.000 001
10–9 nano n 0.000 000 001
10–12 pico p 0.000 000 000 001
10–15 femto f 0.000 000 000 000 001
10–18 atto a
0.000 000 000 000 000
001
10–21 zepto z
0.000 000 000 000 000
000 001
10–24 yocto y
0.000 000 000 000 000
000 000 001

11. ENGLISH SYSTEM
• - is commonly used in English-speaking countries
that is also known as the British System.
Length:
1 foot (ft) = 12 inches
(in)
1 yard (yd) = 3 feet
1 mile (mi) = 5280
feet
1 mile = 1760 yards
Weight:
1 pound (lb) = 16
ounces (oz)
1 ton = 2000 pounds
Capacity:
1 tablespoon (tbsp) = 3
teasponns (tsp)
1 cup (c) = 16
tablespoons
1 cup = 8 fluid ounces
(oz)
1 pint (pt) = 2 cups

12. CONVERSION RATIO (OR UNIT FACTOR)
• While the Metric System simply moves the decimal point to
convert between its measurements' prefixes, the English
System requires a conversion ratio (or unit factor) to move
between measurements. In the Metric System, the prefix itself
gives the needed conversion ratio.

13. • A conversion ratio (or unit factor) is a ratio equal to one. This
ratio carries the names of the units to be used in the
conversion. It can be used for conversions within the English
and Metric Systems, as well as for conversions between the
systems. The conversion ratio is based upon the concept of
equivalent values. In the example below, one foot is substituted
for its equivalent measure of 12 inches.

14. • Example 1:
Let's start with a simple example: convert 3 km to m (3
kilometers to meters). There are 1000 m in 1 km, so the
conversion is easy, but let's follow a system.
The system is:
• Write the conversion as a fraction that equals 1
• Multiply it out (leaving all units in the answer)
• Cancel any units that are both top and bottom

15. • We can write the conversion as a fraction that equals 1:
1000 𝑚
𝟏 𝐤𝐦
= 1
• And it is safe to multiply by 1 (does not affect the answer):
3 km × 1 = 3 km
• so we can do this:
3 km ×
1000 𝑚
𝟏 𝐤𝐦
= 3000 km · m 1 km

16. • The answer looks strange! But we aren't finished yet ... we can
"cancel" any units that are both top and bottom:
• 3000 𝑘𝑚 · 𝑚
𝟏 𝐤𝐦
= 3000 m
• So, 3 km equals 3000 m. Well we knew that, but we want to
follow a system, so that when things get harder we know what
to do!
• And when we do it correctly we get to cancel units that are both
top and bottom, and get a neat answer.

17. •: if we do it wrong (with the conversion
upside down) we get this:
3 km ×
1 𝑘𝑚
𝟏𝟎𝟎𝟎 𝐦
=
3 𝑘𝑚 · 𝑘𝑚
𝟏𝟎𝟎𝟎 𝐦
And that doesn't let us do any cancelling!

18. EXAMPLE 2:
• Let's use this method to solve the km/h to m/s conversion
from the top of the page.
• We will do it in two stages:
• from km/h (kilometers per hour) to m/h (meters per hour),
then
• from m/h (meters per hour) to m/s (meters per second).v

19. • 1. FROM KM/H (KILOMETERS PER HOUR) TO M/H (METERS PER
HOUR)
1 𝑘𝑚
𝐡
×
1000 m
1 km
=
1000 km · m
1 h · km
• Now "cancel out" any units that are both top and
bottom:
1000 𝑘𝑚 · 𝑚𝟏
𝐡 · 𝐤𝐦
=
1000 𝑚
𝟏 𝐡
• It is now in meters per hour.

20. 2. FROM M/H (METERS PER HOUR) TO M/S (METERS PER SECOND)
• To go from m/h (meters per hour) to m/s (meters per second)
we put the "3600 seconds in an hour" conversion "upside down"
because we want an "h" on top (so they will cancel later) :
1000 𝑚
1 h
×
1ℎ
𝟑𝟔𝟎𝟎 𝐬
=
1000𝑚.ℎ
𝟑𝟔𝟎𝟎 𝐡 · 𝐬
• Then "cancel out" any units that are both top and bottom:
1000 𝑚 · ℎ
𝟑𝟔𝟎𝟎 𝐡 · 𝐬
=
1000 𝑚
𝟑𝟔𝟎𝟎 𝐬

21. • And so our anwer is:
1000 𝑚
𝟑𝟔𝟎𝟎 𝐬
= 0.2777... m/s
• Doing it wrong (with the the 3600 seconds/hour the
other way around) gets this:
1000 𝑚
𝟏 𝐡
×
3600 𝑠
𝟏 𝐡
=
1000 × 3600 𝑚 · 𝑠
𝟏 𝐡 · 𝐡
• And there is nothing to cancel!
• So we know we made a mistake, and can correct it.

22. • 23kg convert it into grams
• 23kg ×
1000𝑔
1𝑘𝑔
= 23,000 𝑔
• 250grams convert it into kg
• 250g×
1𝑘𝑔
1000𝑔
= 0.25 kg

23. •30dm converted into meters (m)
•30dm ×
10𝑚
1𝑑𝑚
= 300dm
•850mm convert it into km
• 850mm×
1𝑚
1000𝑚𝑚
×
1𝑘𝑚
1000𝑚
= 0.00085 km

24. •14km you have to convert it
into cm
•14km ×
1000𝑚
1𝑘𝑚
×
100𝑐𝑚
1𝑚
=
1,400,000

25. • 850mm you have to convert it into km
• 850mm ×
1𝑚
1000𝑚𝑚
×
1𝑘𝑚
1000𝑚
=0.00085 km