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Power Builder on Conversion of Units
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It is a fundamental skill in Physics to have a background in converting one quantity to another especially that there
are equations that can only be used if the quantity is expressed in its standard unit. For example, in solving for Current in
Ohms Law (𝐼 = 𝑉/𝑅), Voltage must be expressed in terms of Volts (V) and Resistance in terms of Ohms (Ω).
We must also keep in mind that we may come across two types of system of measurement: Metric and the English
system. We often use Metric compared to the English system especially in Physics. However, from time to time, there are
still some problems that involve English units such as feet, inch, and the like.
Metric system is very much convenient to use due to special unit prefixes (and more appreciable when you have
mastery in scientific notation). With this, the most common approach is the use of a number line and to move the position
of the decimal point to change its unit.
Examples:
1. How many Megabytes (MB) are there in 1 GB?
This means that the decimal point will also be moved
thrice (three times) to the right (same with the
direction of the rabbit)!
1 GB = 1000. MB
Therefore, 1 GB is equivalent to 1000 MB.
2. How many centimeters are there in 3.2 Km?
This means that the decimal point will also be moved five
times to the right (same with the direction of the rabbit)!
3.2 Km = 320000. Cm
Therefore, 3.2 Km is equivalent to 320, 000 cm.
1
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3. How many Farad* are there in 12 pF (picofarad)?
*Farad is a base unit and is a standard unit of Capacitance
Notice that there are 3 jumps that has 3 units interval
already: 3𝑥3 = 9, and then after that 3 additional normal
jumps.
This only means that the decimal point needs to be
moved 12 times to the left (same with the direction of the
rabbit)!
2
12 pF = 0.000000000012 F
12 𝑝𝐹 = 12 × 10!"# 𝐹
Tsk tsk tsk! Too many zeroes!!! It may be too tasking to
write so we can rewrite it into its scientific notation.
Note: The p in the picofarad is rewritten as the base 10
you can see in the conversion unit line. This only applies if
you are converting the unit into its base form (middle of
the conversion line).
Therefore, 12 pF is equivalent to 12 x 10-12 F
On your own, try the following items:
2 cm =
65 dg =
mm
8.509 km =
m
594 mm =
cm
g
6, 050 Dg =
g
562 nC =
C
mg
0.01 mA =
A
MB
900 pm =
nm
s
997 Kw =
w
813,000 mg =
100 mV =
6028 KB =
kg
124.01 g =
V
2 TB =
GB
10.8 ms =
The previous examples involve the base quantities. These are quantities that are distinct in nature and cannot be
defined by other quantities. As such, they are relatively easier to convert from one unit to another. However, in Physics, we
will also be dealing with derived quantities. These quantities are made up of combined base quantities such as in speed,
volume, force and energy. With this, a longer method is necessary.
Examples:
1. The speed of light is 3 × 10$ 𝑚/𝑠; what will this It may be helpful to list down first the conversion
information that we can use:
be in km/h?
1 𝑘𝑚 = 10% 𝑚 = 1000 𝑚
1 ℎ𝑜𝑢𝑟 = 60 𝑚𝑖𝑛𝑠 = 3600 𝑠
We can now start writing down the conversion factors one
at a time. The goal is to be able to cancel out the 𝑚/𝑠 and
turn it into 𝑘𝑚/ℎ:
Simplify:
2. How many cm2 are there in a 10m2 area?
1.08 × 10& 𝑘𝑚/ℎ
Speed of light in km/h
List down the known conversion information:
1 𝑚 = 100 𝑐𝑚
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Since the known conversion information is only in terms of
𝑚" , then we can say that (1𝑚)# = (100 𝑐𝑚)# . Thus,
Note: This technique can also be applied in terms of volume.
Simplify, we get
10' 𝑐𝑚# or 100,000 𝑐𝑚#
Some additional information on conversion:
VOLUME
1 𝐿 = 1000 𝑚𝐿
1 𝑚𝐿 = 1𝑐𝑚%
3
TEMPERATURE
9
𝐹 = 𝐶 × + 32
5
5
𝐶 = (𝐹 − 32)
9
𝐾 = 𝐶 + 273.15
On your own, try the following items:
37°F =
°C
0.21 L =
mL
9896 mL =
L
L
40405 mL =
m3
4696 m3 =
L
9748 cm3 =
-79 °C =
°F
100 °C =
K
37.25°C =
°F
0K=
°F
Comprehension Check:
1.
2.
3.
4.
What system of measurement can be expressed in bases of 10 thus assigning distinct prefixes to some of this?
What system of measurement is known for the units such as feet, inch, and pounds?
What do we call the quantities made up of two or more base units?
Using the number line technique, to convert a unit to its larger counterpart, the decimal point is moved to the ( left,
right ).
5. Using the number line technique, to convert a unit to its smaller counterpart, the decimal point is moved to the (
left, right ).
- End -
© Callo2020
Power Builder on Conversion of Units Key
20
2 cm =
6.5
65 dg =
813,000 mg =
100 mV =
6028 KB =
mm
g
0.813
kg
8.509 km =
8509
6, 050 Dg =
60500
124.01 g = 124010
0.1
V
2 TB =
0.006028
GB
10.8 ms =
2x10
6
0.0108
m
g
mg
MB
s
594 mm =
562 nC =
59.4
5.62x10
0.01 mA = 1x10
900 pm =
cm
11
C
-5
0.9
A
nm
997 Kw = 997000
w
4
37°F =
4696 m3 =
-79 °C =
2.78
4696000
-110.2
Comprehension check:
1. Metric system
2. English system
3. Derived Quantities
4. Left
5. Right
°C
0.21 L =
210
9.748
mL
L
9748 cm3 =
L
°F
100 °C =
373.15
K
37.25°C =
99.05
°F
9896 mL =
9.896
40405 mL = 0.4041
0 K = -459.67 °F
L
m3