Units, Unit Conversion and Significant Digits
SPH3U
Ms. Kueh
Scientific Notation
Rewrite the following numbers in scientific notation:
Thickness of plastic: 0.000 01 𝑚
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Diameter of a hydrogen atom: 0.000 000 005 3 𝑐𝑚
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Mass of H2O in Lake Erie: 12 000 000 000 000 000 𝑘𝑔
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Scientific Nomenclature
Name
length
time
velocity (speed)
mass
frequency
wavelength
Prefixes
(Systeme Internationale - SI)
Symbol
𝑑, 𝑥, 𝑦, 𝑙, ℎ, 𝑟
𝑡
𝑣
𝑚
ƒ
𝜆
Base Unit
metre
seconds
metres/second
grams
Hertz (cycles/s)
metre
Unit symbol
𝑚
𝑠
𝑚/𝑠
𝑔
𝐻𝑧
𝑚
(Note: You must know these!)
Prefix
Symbol
Factor difference
tera
𝑇
1012 = 1000000000000
giga
𝐺
109 = 1000000000
mega
𝑀
106 = 1000000
kilo
𝑘
103 = 1000
centi
𝑐
10−2 = 1/100 = 0.01
milli
𝑚
10−3 = 1/1000 = 0.001
micro
µ
10−6 = 0.000001
nano
𝑛
10−9 = 0.000000001
* Physics formulas generally use mass in kilograms
Unit Conversions
1. Mass
1.23 𝑘𝑔 𝑡𝑜 𝑔
2. Time
0.0276 𝑠 𝑡𝑜 𝑚𝑠
17 years into minutes
3. Distance
555 𝑚𝑚 𝑡𝑜 𝑐𝑚
4. Computer Units
1.5 𝑇𝑏𝑦𝑡𝑒 𝑡𝑜 𝑀𝑏𝑦𝑡𝑒𝑠
5. Area
3.456 𝑀𝑚2 𝑡𝑜 𝑘𝑚2
6. Volume
5 𝑚3 𝑡𝑜 𝑚𝑚3
Example 1
The density of helium gas is 0.18𝑔/𝐿. What is the volume of 50𝑔 of helium?
Example 2
Convert 70 𝑘𝑚/ℎ to 𝑚/𝑠.
Try it yourself: Convert 721 lbs per week into kg per second. (1 lb = 0.45 kg.)
*More practice on the website lkueh.wordpress.com
Significant Digits
 The number of significant digits in a value is the number of digits that are known with
certainty. These include:
1. All non-zero digits. (1 to 9)
Ex: 12145 𝑚
5 significant digits
2. All zeros between non-zero digits.
Ex: 1204 𝑚
4 significant digits
3. All trailing zeros after a decimal.
Ex: 54.0200 𝑚
6 significant digits
4. All trailing zeros before a decimal.
Ex: 3600. 𝑚
4 significant digits
5. In scientific notation, all significant digits are included.
6. Any trailing zeros without a decimal, if the value is a known measurement.
Example: 27000 𝑚 5 sig digits if specified or 2 sig digits otherwise.
***This is why scientific notation is clearer!
7. All digits in counted or defined values are significant. Example: 20 cats 2 sig digits
Note: In a measurement with a decimal point, zeroes placed before other digits are NOT
significant. Example
0.00048 𝑚 has 2 significant digits.
How many significant digits are in the following?
a) 3211 𝑚
b) 32011 𝑚
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c) 32110 𝑚
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d) 32110. 𝑚 ____
e) 3.211 × 102 𝑚
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f) 3.2110 × 102 𝑚
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g) 32.07 𝑚
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h) 0.0041 𝑔
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i) 5 𝑥 105 𝑘𝑔
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j) 6400 𝑠
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k) 240 people
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l) −3.0450 × 10−5 𝐶 ____
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Calculating with Measurements
Adding and Subtracting:
Add (or subtract) the numbers as usual, then round the answer to the same decimal
place as the least-accurate number.
Example
13.214 + 234.6 + 7.0350 + 6.38
Multiplying and Dividing:
Multiply (or divide) the numbers as usual, then round the answer to the same number
of significant digits as the least-accurate number.
Example 1
16.235 × 0.217 × 5
Example 2
0.00435 × 4.6
a) 2.301 𝑚 + 1.4444 𝑚
b) 321.66 𝑚 − 21.1 𝑚
c) 1.2 𝑚 × 3.33 𝑚
d) 1.00000 𝑚 ÷ 3 𝑠
e)
6.3 𝑘𝑔 × 2.34 𝑚
1.748 𝑠
f) 674.3 𝑐𝑚 − 2.554 𝑚 − 1583.34 𝑚𝑚