Question

give the correct number of significant figures in the following measurements:

1. 345 cm
2. 0.93 mm
3. 340 l
4. 0.097 ml
5. 39.5 g
6. 0.09305 kg
7. 38.05 m
8. 0.00760 m
9. 139.0 mm
10. 1.008 m
11. 10001 m
12. 15.96 kg
13. 10100 ml
14. 1.95 * 10^(-8) km
15. 89050. km
16. 3.9 * 10^(3) ml

round the following measurements off to the indicated number of sig. figs.:

1. 6.789456 ml (5)
2. 7.000999 cm (3)
3. 10.3245 km (5)
4. 3.6759091 m (6)
5. 1770.3245 l (4)
6. 23.4569043 cm (5)
7. 0.000087345 kg (3)
8. 0.03678467 l (5)
9. 100000089 cm (5) 1.000 * 10^(8)
10. 32003.034 g (6)
11. 1.000345 kg (4)
12. 32.45693 g (5)
13. 3.27983 * 10^(-8) g (3)
14. 4.93246 * 10^(3) l (4)
15. 9.9999 * 10^(-8) cm (3)
16. 3.45678 sec (4)

express the following measurements in scientific notation:

1. 1000 000 000 m
2. 0.000 000 000 1 m
3. 346545 g
4. 984 l
5. 54851 kg
6. 4456 km
7. 0.15163 cm
8. 0.00041 m
9. 0.00005468 km
10. 150560. l
11. 0.416588 g
12. 0.000215 km
13. 2.454686 sec
14. 0.00516 l
15. 0.5418561 m
16. 1516138.5 g

Explanation:

Step1: Recall significant - figures rules

Non - zero digits are always significant. Zeros between non - zero digits are significant. Leading zeros (zeros before non - zero digits) are not significant. Trailing zeros in a number with a decimal point are significant.

Step2: Determine significant figures for each number

1. 345 cm: 3 significant figures (all non - zero digits)
2. 0.93 mm: 2 significant figures (non - zero digits, leading zero not significant)
3. 340 L: 2 significant figures (trailing zero without decimal is not significant)
4. 0.097 mL: 2 significant figures (leading zeros not significant)
5. 39.5 g: 3 significant figures (all non - zero digits)
6. 0.09305 kg: 4 significant figures (leading zeros not significant, zero between non - zero digits is significant)
7. 38.05 m: 4 significant figures (all digits are significant)
8. 0.00760 m: 3 significant figures (leading zeros not significant, trailing zero with decimal is significant)
9. 139.0 mm: 4 significant figures (trailing zero with decimal is significant)
10. 1.008 m: 4 significant figures (zeros between non - zero digits are significant)
11. 10001 m: 5 significant figures (zeros between non - zero digits are significant)
12. 15.96 kg: 4 significant figures (all non - zero digits)
13. 10100 mL: 3 significant figures (trailing zeros without decimal are not significant)
14. 1.95×10⁻⁸ km: 3 significant figures (all digits in the coefficient are significant)
15. 89050. km: 5 significant figures (trailing zero with decimal is significant)
16. 3.9×10³ mL: 2 significant figures (all digits in the coefficient are significant)

Step3: Recall rounding rules

If the digit to be removed is less than 5, the preceding digit is left unchanged. If the digit to be removed is 5 or greater, the preceding digit is increased by 1.

1. 6.789456 mL (5): 6.7895
2. 7.000999 cm (3): 7.00
3. 10.3245 km (5): 10.325
4. 3.6759091 m (6): 3.67591
5. 1770.3245 L (4): 1770
6. 23.4569043 cm (5): 23.457
7. 0.000087345 kg (3): 0.0000873
8. 0.03678467 L (5): 0.036785
9. 100000089 cm (5): 1.0000×10⁸
10. 32003.034 g (6): 32003.0
11. 1.000345 kg (4): 1.000
12. 32.45693 g (5): 32.457
13. 3.27983×10⁻⁸ g (3): 3.28×10⁻⁸
14. 4.93246×10³ L (4): 4.932×10³
15. 9.9999×10⁻⁸ cm (3): 1.00×10⁻⁷
16. 3.45678 sec (4): 3.457

Step4: Recall scientific - notation rules

Scientific notation is of the form a×10ⁿ, where 1≤|a|<10 and n is an integer.

1. 1000000000 m: 1×10⁹ m
2. 0.000000001 m: 1×10⁻⁹ m
3. 346545 g: 3.46545×10⁵ g
4. 984 L: 9.84×10² L
5. 54851 kg: 5.4851×10⁴ kg
6. 4456 km: 4.456×10³ km
7. 0.15163 cm: 1.5163×10⁻¹ cm
8. 0.00041 m: 4.1×10⁻⁴ m
9. 0.00005468 km: 5.468×10⁻⁵ km
10. 150560. L: 1.5056×10⁵ L
11. 0.416588 g: 4.16588×10⁻¹ g
12. 0.000215 km: 2.15×10⁻⁴ km
13. 2.454686 sec: 2.454686×10⁰ sec
14. 0.00516 L: 5.16×10⁻³ L
15. 0.5418561 m: 5.418561×10⁻¹ m
16. 1516138.5 g: 1.5161385×10⁶ g

Answer:

1. 3
2. 2
3. 2
4. 2
5. 3
6. 4
7. 4
8. 3
9. 4
10. 4
11. 5
12. 4
13. 3
14. 3
15. 5
16. 2
17. 6.7895
18. 7.00
19. 10.325
20. 3.67591
21. 1770
22. 23.457
23. 0.0000873
24. 0.036785
25. 1.0000×10⁸
26. 32003.0
27. 1.000
28. 32.457
29. 3.28×10⁻⁸
30. 4.932×10³
31. 1.00×10⁻⁷
32. 3.457
33. 1×10⁹ m
34. 1×10⁻⁹ m
35. 3.46545×10⁵ g
36. 9.84×10² L
37. 5.4851×10⁴ kg
38. 4.456×10³ km
39. 1.5163×10⁻¹ cm
40. 4.1×10⁻⁴ m
41. 5.468×10⁻⁵ km
42. 1.5056×10⁵ L
43. 4.16588×10⁻¹ g
44. 2.15×10⁻⁴ km
45. 2.454686×10⁰ sec
46. 5.16×10⁻³ L
47. 5.418561×10⁻¹ m
48. 1.5161385×10⁶ g