Question

determine the number of significant figures in each of these numbers.

number\tsignificant figures
1.\t357
3.\t51015
5.\t0.0007
7.\t5050
9.\t6.8×10³
11.\t33.303
13.\t15.0×10⁻⁵
15.\t0.70070
17.\t0.02
19.\t0

number\tsignificant figures
2.\t10000
4.\t6.060×10⁻²
6.\t4.556×10⁻⁹
8.\t5050.0
10.\t0.002110
12.\t170
14.\t0.7007
16.\t4206
18.\t10.01
20.\t0.0

Explanation:

Step1: Non - zero digits are significant

For 357, all three non - zero digits are significant. So the number of significant figures is 3.

Step2: Trailing zeros in a whole number without a decimal point may or may not be significant

For 10000, it is ambiguous. But usually, it is considered 1 significant figure.

Step3: All digits in a non - exponential number are significant

For 51015, all five digits are significant. So the number of significant figures is 5.

Step4: In scientific notation, all digits in the coefficient are significant

For 6.060×10⁻², the coefficient is 6.060, so there are 4 significant figures.

Step5: Leading zeros are not significant

For 0.0007, only the 7 is significant, so 1 significant figure.

Step6: In scientific notation, all digits in the coefficient are significant

For 4.556×10⁻⁹, the coefficient 4.556 has 4 significant figures.

Step7: Trailing zeros in a number with a non - zero digit before them are significant if there is a decimal point

For 5050, it has 3 significant figures. For 5050.0, it has 5 significant figures.

Step8: In scientific notation, all digits in the coefficient are significant

For 6.8×10³, the coefficient 6.8 has 2 significant figures.

Step9: Trailing zeros after a non - zero digit and after a decimal point are significant

For 0.002110, it has 4 significant figures.

Step10: All non - zero digits and zeros between non - zero digits are significant

For 33.303, it has 5 significant figures.

Step11: Trailing zeros in a number with a decimal point are significant

For 170, it has 2 significant figures. For 15.0×10⁻⁵, the coefficient 15.0 has 3 significant figures.

Step12: All non - zero digits and zeros between non - zero digits are significant

For 0.7007, it has 4 significant figures.

Step13: Trailing zeros after a non - zero digit and after a decimal point are significant

For 0.70070, it has 5 significant figures.

Step14: All non - zero digits and zeros between non - zero digits are significant

For 4206, it has 4 significant figures.

Step15: Leading zeros are not significant

For 0.02, it has 1 significant figure.

Step16: All non - zero digits and zeros between non - zero digits are significant

For 10.01, it has 4 significant figures.

Step17: Zero alone has 0 significant figures

For 0, it has 0 significant figures.

Step18: Leading zeros are not significant

For 0.0, it has 0 significant figures.

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. 0