Question

rules significant figures

1. non - zeros are significant:

a. 565 - 3 sig figs

1. zeros in the middle are significant:

a. 5005 - 4 sig figs

1. beginning zeros - not significant:

a. 0.00489 - 3 sig figs

1. zeros after the number - only significant with a decimal:

a. 5400 - 2 sig figs
b. 5400.00 - 6 sig figs
addition & subtraction rules

• round the answer to the least precise place (the least decimal places)

1.0236
+ 1.6
2.6236
2.6
multiplication & division rules

• round the answer to the smallest # of sig figs in the problem

-2.8723
× 4.6
4.9568
4.6
how precise?
determine the number of significant figures in each of these numbers.
number significant figures number significant figures

1. 357 2. 10000
2. 51015 4. 6.060×10⁻²
3. 0.0067 6. 4.556×10³
4. 5050 8. 5050.0
5. 6.8×10⁵ 10. 0.002110
6. 33.303 12. 170
7. 15.0×10⁻³ 14. 0.7007
8. 0.70070 16. 4206
9. 0.02 18. 10.01
10. 0 20. 0.0

Explanation:

Step1: Apply non - zeros rule

For 357, all non - zero digits are significant. So it has 3 significant figures.

Step2: Analyze trailing zeros without decimal

For 10000, trailing zeros without a decimal are not significant. So it has 1 significant figure.

Step3: Consider zeros in the middle

For 51015, zeros in the middle are significant. So it has 5 significant figures.

Step4: Analyze scientific notation

For \(6.060\times10^{-3}\), all digits in the coefficient are significant. So it has 4 significant figures.

Step5: Analyze leading zeros

For 0.0067, leading zeros are not significant. So it has 2 significant figures.

Step6: Analyze trailing zeros with decimal

For 5050.0, all digits are significant. So it has 5 significant figures.

Step7: Analyze scientific notation

For \(6.8\times10^{3}\), it has 2 significant figures.

Step8: Analyze trailing zeros with decimal

For 0.002110, leading zeros are not significant, and trailing zeros with a decimal are significant. So it has 4 significant figures.

Step9: Analyze all digits

For 33.303, all digits are significant. So it has 5 significant figures.

Step10: Analyze trailing zeros without decimal

For 170, trailing zeros without a decimal are not significant. So it has 2 significant figures.

Step11: Analyze scientific notation

For \(15.0\times10^{3}\), all digits in the coefficient are significant. So it has 3 significant figures.

Step12: Analyze all digits

For 0.7007, all digits are significant. So it has 4 significant figures.

Step13: Analyze trailing zeros with decimal

For 0.70070, all digits are significant. So it has 5 significant figures.

Step14: Analyze all digits

For 4206, all digits are significant. So it has 4 significant figures.

Step15: Analyze all digits

For 10.01, all digits are significant. So it has 4 significant figures.

Step16: Analyze leading zeros

For 0.02, leading zeros are not significant. So it has 1 significant figure.

Step17: Analyze trailing zeros

For 0.0, leading zeros are not significant, and this number has 0 significant figures.

Step18: Analyze all digits

For 0, it has 0 significant figures.

Answer:

1. 3
2. 1
3. 5
4. 4
5. 2
6. 5
7. 2
8. 4
9. 5
10. 2
11. 3
12. 4
13. 5
14. 4
15. 4
16. 1
17. 0
18. 0