1. SI Units
The worldwide scientific community and most countries currently use an adaptation of the metric system to state measurements. The Système International d’Unités, or SI, uses seven base quantities, which are below.

2. DERIVED UNITS Defined by a combination of base units
Volume: ml = cm3
Speed: m/s
Acceleration:
Force:
𝑚/ 𝑠 2
Newton=𝑘𝑔∙ 𝑚 𝑠 2

3. PREFIXES USED WITH SI UNITS
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Equivalents
For Conversions
Kilo
1000
units
Hecto
100
Deka 10
Basic
Unit
Deci
0.1
Centi
0.01
Milli
0.001
10 −3
10 2
10 3 1

4. Prefixes used with SI Units

5. Dimensional Analysis (AKA Factor Label)
Dimensional analysis is used in choosing conversion factors. A conversion factor is a multiplier equal to 1.
For example, because 1 kg = 1000 g, you can construct the following conversion factors:

6. Conversion Factor Label Practice!
1. Convert 132 cm into km:
132𝑐𝑚 1𝑚 𝑐𝑚 𝑥 10 −3 1𝑚 = km
OR move the decimal 5 places to the left.
Convert 1201 seconds into hours:
1201𝑠 1𝑚𝑖𝑛 60𝑠 𝑥 1ℎ 60𝑚𝑖𝑛 =0.3336h

7. Significant Figures (Digits)
The numbers in measurements are limited by the measuring tool.
Significant figures in a measurement include the known digits plus one estimated digit.

8. 1. What is the 1st measurement?
1.42 cm
2. What is the 2nd measurement?
2.7 cm

9. Counting Significant Figures
RULE 1. All non-zero digits in a measured number are significant. Only a zero could indicate that rounding occurred.
Give the Number of Significant Figures
38.15 cm 4
5.6 ft 2
65.6 lb ___
m ___

10. Leading Zeros
RULE 2. Leading zeros in decimal numbers are NOT significant.
Give the Number of Significant Figures
0.008 mm 1
oz 3
lb __
mL __

11. Sandwiched Zeros
RULE 3. Zeros between nonzero numbers are significant. (They can not be rounded unless they are on an end of a number.)
Give the Number of Significant Figures
50.8 mm 3
2001 min 4
0.702 lb __
m __

12. Trailing Zeros
RULE 4. Trailing zeros in numbers without decimals are NOT significant. They are only serving as place holders.
Give the Number of Significant Figures
25,000 in. 2
200. yr 3
48,600 gal __
25,005,000 g __

13. Learning Check A. Which answers contain 3 significant figures?
1) ) ) 4760
B. All the zeros are significant in
1) ) ) x 103
C. 534,675 rounded to 3 significant figures is
1) ) 535, ) 5.35 x 105

14. Learning Check
In which set(s) do both numbers contain the same number of significant figures?
400.0 and 40
and 150,000
22.0 and 22.00

15. Learning Check
State the number of significant figures in each of the following: A m B L C g D m E. 2,080,000 bees 3 5 7

16. How many sig figs in the following measurements?1) 2) 3)
4) 8.01
5) 23,000,000
6) x 107 7)
Ans.1) 5 2) 6 3) 2 4) 3 5) 2 6) 3 7)4

17. Adding and Subtracting
The answer has the same number of decimal places as the measurement with the fewest decimal places one decimal place two decimal places answer 26.5 one decimal place

18. Learning Check
In each calculation, round the answer to the correct number of significant figures.
A =
1) ) ) 257
B =
1) ) ) 40.7

19. Multiplying and Dividing
Round (or add zeros) to the calculated answer until you have the same number of significant figures as the measurement with the fewest significant figures.

20. Learning Check A. 2.19 X 4.2 = 1) 9 2) 9.2 3) 9.198 B. 4.311 ÷ 0.07 =
1) ) )
B ÷ =
1) ) ) 60
C X =
X 0.060
1) ) )

21. Reading a Meterstick
. l I I I I cm
First digit (known) = 2.?? cm
Second digit (known) = ? cm
Third digit (estimated) between
Length reported = cm
or 2.74 cm
or 2.76 cm

22. Known + Estimated Digits
In 2.76 cm…
Known digits 2 and 7 are 100% certain
The third digit 6 is estimated (uncertain)
In the reported length, all three digits (2.76 cm) are significant including the estimated one

23. Learning Check . l8. . . . I . . . . I9. . . .I . . . . I10. . cm
What is the length of the line?
1) cm
2) cm
3) cm

24. Zero as a Measured Number
. l I I I I cm
What is the length of the line?
First digit ?? cm
Second digit ? cm
Last (estimated) digit is cm