1. Unit 1 Significant Figures in Measurements

2. Scientific Measurements
When using a scale you read the value on the closest line and ONE guess.

3. You Try!
Measure the length and width of your paper in mm. Record the correct number of significant figures.

4. Scientific Measurements
Measurement includes value of closest line plus one more decimal “guess”.
Here it would be 4.7x.
We know it is a little more than 4.7, so the “x” is the guess.

5. Scientific Measurements
Liquid measurements taken from bottom of meniscus.

6. Scientific Measurements
Measurement includes value of closest line plus one more decimal “guess”.
6.6x mL
I would say mL

7. Scientific Measurements
For digital devices, record ALL decimals
Temperature measurement is 13.0°C (not 13°C)

8. SIGNIFICANT FIGURES
Read each measurement:
28 mL
28.3 mL
28.32 mL

9. Precision v. Accuracy
Precision –how closely individual measurements agree (repeatability)
Accuracy – how closely individual measurements agree with the correct or “true” value (bullseye)

10. Significant Figures 56,400,000 Is there a decimal? PACIFIC (Present)
ATLANTIC (Absent)
Start from LEFT & count all #s from first nonzero
Start from RIGHT & count all #s from first nonzero
56,400,000
4 sig figs
3 sig figs

11. You Try! How many sig figs in the following: Examples: a) 1001 km
b) m
c) 129,870 m
d) km
e) L
f) 6.02 x 1023 atoms
g) 20,000 cm
h) g
Number of Significant Figures:
a) 4
b) 4
c) 5
d) 1
e) 4
f) 3
g) 1
h) 2

12. Rounding Tips:
When rounding number greater than or equal to 5: round up.
Ex: = 5.8
4.89 = 4.9
When rounding number less than 5: round down.
Ex: = 5.2
4.12 = 4.1

13. Rounding Round each of these to 2 sig figs: Examples: a) 34.00 m
b) 34,000 m
c) 129,870 m
d) km
e) L
f) 6.02 x 1023 atoms
g) 20,000 cm
h) 1001 km
Number of Significant Figures:
a) 34 m
b) 34,000 m
c) 130,000 m
d) km
e) 1.0 L
f) 6.0 x 1023 atoms
g) 2.0 x 104 cm
h) 1.0 x 103 km

14. CALCULATIONS WITH SIG FIGS
RULE: When multiplying or dividing, round the final answer to the measurement with the smallest number of significant figures.
Examples:
cm x cm = cm²
= 73.1 cm²
2. (1.13 m)( m) = m²
= 5.79 m²
cm² / cm = cm
= cm

15. CALCULATIONS WITH SIG FIGS
RULE: When adding or subtracting, round the answer to the smallest number of decimal places.
Examples: 1) cm cm cm cm = cm

16. You Try! Addition Multiplication 165.5 cm + 8 cm + 4.37 cm = 177.87 cm
2.6 cm x 3.78 cm = cm
= 178 cm
9.828 cm2
= 9.8 cm2

17. CALCULATIONS WITH SIG FIGS Summary
Multiplying or dividing: round to the measurement with the smallest number of significant figures.
Adding or subtracting: round the answer to the smallest number of decimal places.

18. You Try!
Calculate the area (length x width) of your paper using the correct number of sig figs.