Question

how many significant figures do the following numbers have? 1) 956 2) 2.1390 3) 4390 4) 0.500 5) 500 6) 5.9×10⁴ 7) 0.40001 8) 1.7×10⁻³ 9) 650. 10) 4.150×10⁻⁴ 11) 3670000 12) 0.0000620 13) 96 14) 678.02400 15) 30000 16) 0.002 17) 91530 18) 0.000400 19) 6.0 20) 352

Explanation:

Step1: Non - zero digits are significant

For 956, all three non - zero digits are significant. So it has 3 significant figures.

Step2: Non - zero and trailing zeros after decimal

For 2.1390, non - zero digits 2, 1, 3, 9 and the trailing zero after the decimal are significant. So it has 5 significant figures.

Step3: Trailing zeros without decimal are ambiguous

For 4390, assuming no other context, it has 3 significant figures (4, 3, 9).

Step4: Leading zeros are not significant

For 0.500, leading zero is not significant, and the non - zero digit 5 and two trailing zeros are significant. So it has 3 significant figures.

Step5: Trailing zeros without decimal (ambiguous)

For 500, assuming no other context, it has 1 significant figure (5).

Step6: Scientific notation significant figures

For 5.9×10⁴, the significant figures are in the coefficient 5.9, so it has 2 significant figures.

Step7: Non - zero and zeros between non - zeros

For 0.40001, leading zero is not significant, and non - zero digit 4 and zeros between 4 and 1 are significant. So it has 5 significant figures.

Step8: Scientific notation significant figures

For 1.7×10⁻³, the significant figures are in the coefficient 1.7, so it has 2 significant figures.

Step9: Trailing zero with decimal

For 650., the non - zero digits 6, 5 and the trailing zero with the decimal are significant. So it has 3 significant figures.

Step10: Scientific notation significant figures

For 4.150×10⁻⁴, the significant figures are in the coefficient 4.150, so it has 4 significant figures.

Step11: Trailing zeros without decimal (ambiguous)

For 367000, assuming no other context, it has 3 significant figures (3, 6, 7).

Step12: Leading zeros not significant

For 0.0000620, leading zeros are not significant, and non - zero digits 6, 2 and the trailing zero are significant. So it has 3 significant figures.

Step13: Non - zero digits

For 96, both non - zero digits are significant. So it has 2 significant figures.

Step14: All digits are significant

For 678.02400, all digits are significant. So it has 8 significant figures.

Step15: Trailing zeros without decimal (ambiguous)

For 30000, assuming no other context, it has 1 significant figure (3).

Step16: Leading zeros not significant

For 0.002, leading zeros are not significant, and the non - zero digit 2 is significant. So it has 1 significant figure.

Step17: Non - zero digits and trailing zero

For 91530, assuming no other context, it has 4 significant figures (9, 1, 5, 3).

Step18: Leading zeros not significant

For 0.000400, leading zeros are not significant, and non - zero digit 4 and two trailing zeros are significant. So it has 3 significant figures.

Step19: Non - zero digit and trailing zero with decimal

For 6.0, non - zero digit 6 and the trailing zero with the decimal are significant. So it has 2 significant figures.

Step20: Non - zero digits

For 352, all three non - zero digits are significant. So it has 3 significant figures.

Answer:

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