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. 5460 - 3 sig figs
b. 5400.00 - 6 sig figs
addition & subtraction rules

• round the answer to the least precise number (drop off decimal area)

1.0236
+ 1.6
2.6236
2.6
multiplication & division rules

• round the answer to the same number of sig figs as the problem

2.8723
x 1.6
4.59568
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. 6.050×10^4
3. 0.0007 6. 4,556×10^7
4. 5050 8. 5050.0
5. 6.8×10^3 10. 0.002110
6. 33.303 12. 170
7. 15.0×10^5 14. 0.7007
8. 0.70070 16. 4206
9. 0.02 18. 10.01
10. 0 20. 0.0

Explanation:

Step1: Apply rule 1 for 357

Non - zeros are significant, so 357 has 3 significant figures.

Step2: Apply rule 1 for 10000

Trailing zeros without a decimal are not significant, so 10000 has 1 significant figure.

Step3: Apply rule 1 and 2 for 51015

Non - zeros and zeros in the middle are significant, so 51015 has 5 significant figures.

Step4: Apply rule 1 and 2 for $6.050\times10^{2}$

Non - zeros, zeros in the middle and trailing zeros with a decimal are significant, so $6.050\times10^{2}$ has 4 significant figures.

Step5: Apply rule 3 for 0.0007

Beginning zeros are not significant, so 0.0007 has 1 significant figure.

Step6: Apply rule 1 for $4.556\times10^{7}$

Non - zeros are significant, so $4.556\times10^{7}$ has 4 significant figures.

Step7: Apply rule 1 and 2 for 5050

Non - zeros and zeros in the middle are significant, so 5050 has 3 significant figures (no decimal).

Step8: Apply rule 1, 2 and 4 for 5050.0

Non - zeros, zeros in the middle and trailing zeros with a decimal are significant, so 5050.0 has 5 significant figures.

Step9: Apply rule 1 for $6.8\times10^{3}$

Non - zeros are significant, so $6.8\times10^{3}$ has 2 significant figures.

Step10: Apply rule 3 and 4 for 0.002110

Beginning zeros are not significant, trailing zeros with a decimal are significant, so 0.002110 has 4 significant figures.

Step11: Apply rule 1 and 2 for 33.303

Non - zeros and zeros in the middle are significant, so 33.303 has 5 significant figures.

Step12: Apply rule 1 for 170

Trailing zeros without a decimal are not significant, so 170 has 2 significant figures.

Step13: Apply rule 1, 2 and 4 for $15.0\times10^{ - 5}$

Non - zeros, zeros in the middle and trailing zeros with a decimal are significant, so $15.0\times10^{ - 5}$ has 3 significant figures.

Step14: Apply rule 1 and 2 for 0.7007

Non - zeros and zeros in the middle are significant, so 0.7007 has 4 significant figures.

Step15: Apply rule 1 and 2 for 0.70070

Non - zeros, zeros in the middle and trailing zeros with a decimal are significant, so 0.70070 has 5 significant figures.

Step16: Apply rule 1 and 2 for 4206

Non - zeros and zeros in the middle are significant, so 4206 has 4 significant figures.

Step17: Apply rule 3 for 0.02

Beginning zeros are not significant, so 0.02 has 1 significant figure.

Step18: Apply rule 1 and 2 for 10.01

Non - zeros and zeros in the middle are significant, so 10.01 has 4 significant figures.

Step19: Apply rule 1 for 0

0 has 0 significant figures.

Step20: Apply rule 4 for 0.0

Trailing zeros with a decimal are significant, but this is just 0 with a decimal, so 0.0 has 1 significant figure.

Answer:

1. 3
2. 1
3. 5
4. 4
5. 1
6. 4
7. 3
8. 5
9. 2
10. 4
11. 5
12. 2
13. 3
14. 4
15. 5
16. 4
17. 1
18. 4
19. 0
20. 1