1. Review of Essential Skills:
SI Units, Scientific Notation, Significant Figures & Rounding

2. SI Units
Standard Unit: Metric is usually the preferred unit in science.
Metric referred to as “S.I.” (System Internationale)
Also known as MKS system
Metres: Standard unit for distance
Kilograms: Standard unit for mass
Seconds: Stanard unit for time
Some examples: Speed (m/s), Volume (m3)

3. Scientific Notation
Often in Physics, calculations require the usage of large figures, scientific notation makes these calculations easier.
Some examples:
m = x 107 m
s = x 10-5 s
Decimal moved left?
Positive Exponent
Decimal moved right?
Negative Exponent

4. SN Recipe Place a decimal to get a number between 1 and 10.
Multiply by 10.
Add a power/exponent to the 10 based on the number of times you moved the decimal.

5. Eg.1: Convert each number below to scientific notation.
Eg.2: Convert each number to real notation.
a) km
b) s = =
= 6.73 x 10-2 km
= x 108 s
a) 4.5 x 103 m
b) x 10-7 s
= 45 00 =
= m
= s

6. Significant Figures (“Sig Figs”)
Values that are significant to a measurement
Gives certainty to any measure.
Guidelines
Count from left to right, beginning with the first non-zero digit.
Number
# of Significant Digits
345 3
457.35 5

7. 2. Zeros at beginning are never significant.
Number
Sig Figs
0.235 3
0.003 1

8. 3. All non-zero digits in a number are significant.
Sig Figs
1.1223 5
76.2 3

9. 4. Zeros between digits are significant.
Number
Sig Figs
107.05 5 4

10. 5. Zeros at the end of a number with a decimal point are significant.
Sig Figs
10.0 3
303.0 4

11. 6. Zeros at the end of a number without a decimal are not significant.
Sig Figs
5400 2 1

12. 7. All digits in the coefficient of a number written in scientific notation are significant.
Sig Figs
5.4 x 103 2
5.40 x 103 3
5.400 x 103 4

13. Significant Figures (“Sig Figs”)
Values that are significant to a measurement.
Leading / trailing zeros are typically placeholders.
Eg.3: State the number of sig figs in each case.
Value
# of Sig Figs
Comment
32000 m m
15000 m
100.0 m m 2
Last 3 zeros are placeholders 5
Last 2 zeros are placeholders ~ 4
Tilde (~) indicates last significant figure
Numbers recorded AFTER decimal place wouldn’t be recorded unless significant 4 5
Leading zeros not significant, last two digits are part of the measurement

14. Rounding Rules
Very simple set of rules with the exception of numbers terminating in 5
Rules:
Number terminates in value > 5: Round up
Number terminates in value < 5: Round down
Number terminates in 5:
Round to ensure the rounded value is an even number.

15. Eg.4: Round to the specific number of sig figs.
Since the last example is terminated by a non-zero number, the “5 rule” does not apply…
Value
Sig Figs to Round To
Answer
5.637 3
4.6337
3.65 2
3.55
3.5500
3.651
5.64
4.63
3.6
3.6
3.6
3.7

16. Eg.5: Consider the following data set: [1.5, 2.5, 3.5, 4.5]
Why the “5 rule”?
Automatically rounding up skews data in one direction.
Eg.5: Consider the following data set:
[1.5, 2.5, 3.5, 4.5]
Original sum: = 12
Rounding Rule for 0.5
Rounded Set
Sum
Round up
“5 Rule”
[2,3,4,5] 14
[2,2,4,4] 12