1. Scientific Measurement
Chapter 2 Sec 2.3
Scientific Measurement

2. What is the measured value?
Significant Figures in Measurement all known digits + one estimated digit

3. Estimating Measurements
The hundredths place is somewhat uncertain. Leaving it out would be misleading. Must estimate cm or 6.36cm
Probably not EXACTLY 6.35 cm
Within .01 cm of actual value.
6.35 cm ± .01 cm
6.34 cm to 6.36 cm

4. H. Rules of Significant Figures

5. H. Rules of Significant Figures
1. Every nonzero digit in a measurement is significant (1-9). Ex: 831 g = 3 sig figs
2. Zeros in the middle of a number are always significant. Ex: 507 m = 3 sig figs
3. Zeros at the beginning of a number are NEVER significant. Ex: g = 2 sig figs

6. H. Rules of Significant Figures
4. Zeros at the end of a number are only significant if a decimal point is present.
Ex: g =
240. =
2400 g =
g =
4 sig figs
3 sig figs
2 sig figs

7. Sig Fig Practice #1 How many significant figures in the following?
5 sig figs
17.10 kg 
4 sig figs
100,890 L 
5 sig figs
These all come from some measurements
3.29 x 103 s 
3 sig figs
cm 
2 sig figs
3,200,000 mL 
2 sig figs
This is a counted value
5 dogs 
unlimited

8. Sec 2.3 Significant Figures

9. Sec 2.3 Practice Problems – Significant Figures

10. I. Significant Figures in Calculations
1. A calculated answer can only be as precise as the least precise measurement from which it was calculated
2. Exact numbers never affect the number of significant figures in the results of calculations (unlimited sig figs)
a) counted numbers Ex: 17 beakers
b) exact defined quantities Ex: 60 sec = 1min
Ex: avagadro’s number = 6.02 x 1023

11. I. Significant Figures in Calculations
3. multiplication and division: answer can have no more sig figs than least number of sig figs in the measurements used.

12. I. Significant Figures in Calculations
4. addition and subtraction:
a) decimal - answer can have no more decimal places than the least number of decimal places in the measurements used. (not sig figs)
b) whole number- answer rounded so final sig fig is in the same place as the leftmost uncertain digit.
ex: = 5800

13. Significant Figures, continued
Section 3 Using Scientific Measurements
Chapter 2
Significant Figures, continued
Rounding

14. Rounding Sig Fig Practice #1
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 23 m2
100.0 g ÷ 23.7 cm3
4.22
g/cm3
0.02 cm x cm
0.05
cm2
710 m ÷ 3.0 s
240
m/s

15. Rounding Practice #2 Calculation Calculator says: Answer
3.24 m m
10.24
10.2 m
100.0 g g
76.26
76.3 g
0.02 cm cm
2.398
2.40 cm
710 m -3.4 m
706.6
707 m

16. Rounding Practice #3 Calculation Calculator says: Answer 324 m + 70 m
394
390 m
1300 g g
1063
1100 g
1250 cm + 25 cm
1275
1280cm
odd # preceding 5
720 m -35 m
685
680 m
even # preceding 5

17. Rounding Practice #4 Calculation Calculator says: Answer
3.25 m m
3.95
4.0 m
odd # preceding 5
1.55 g g
1.25
1.2 g
even # preceding 5
21.25 g ÷ 7.2 cm3
3.0 g/cm3
55.00 m x m
1842.5
1842 m2

18. Sec 2.3 Practice Problems – Significant Figures

19. Sec 2.3 Practice Problems – Significant Figures

20. Scientific Notation
An expression of numbers in the form m x 10n where m (coefficient) is equal to or greater than 1 and less than 10, and n is the power of 10 (exponent)

21. J. Rules of Scientific Notation
1. Multiplication – multiply the coefficients and add the exponents
Ex: (3x104) x (2x102) = (3x2) x = 6 x 106
2. Division – divide the coefficients and subtract the exponent in the denominator from the exponent in the numerator
Ex: (3.0x105)/(6.0x102) = (3.0/6.0) x = 0.5 x 103 = 5.0 x 102

22. J. Rules of Scientific Notation
3. Addition – exponents must be the same and then add the coefficients
Ex: (5.4x103) + (8.0x102)
(8.0x102) = (0.80x103)
(5.4x103) + (0.80x103) = ( ) x 103 = 6.2 x 103
4. Subtraction – exponents must be the same and then subtract the coefficients
Ex: (5.4x103) - (8.0x102)
(5.4x103) - (0.80x103) = ( ) x 103 = 4.6 x 103

23. Sec 2.3 Practice Problems – Scientific Notation

25. Chapter 2 Direct Proportions
Section 3 Using Scientific Measurements
Chapter 2
Direct Proportions
Two quantities are directly proportional to each other if dividing one by the other gives a constant value.
read as “y is proportional to x.”

26. Direct Proportion
A straight line graph results from the relationship of direct proportion y x
= k
The line is extrapolated to pass through the origin

27. Chapter 2 Inverse Proportions
Section 3 Using Scientific Measurements
Chapter 2
Inverse Proportions
Two quantities are inversely proportional to each other if their product is constant.
read as “y is proportional to 1 divided by x.”

28. Inverse Proportion xy = k
A graph of variables that are inversely proportional produces a curve called a hyperbola
xy = k

29. Vocabulary 14. accuracy 15. precision 16. percent error
17. significant figures
18. scientific notation
19. directly proportional
20. inversely proportional