Question

how many sig figs? determine the number of sig figs for each of the following measurements. 14) 0.0120 m 15) 100.5 ml 16) 350. cm² 17) 1000 kg 18) 0.0020700 dm determine the number of sig figs for each of the following measurements. 23) 0.000150 l 24) 998,870 cm³ 25) 1.000×10⁴ kg 26) 23,500 mg round the following measurements to the specified number of sig figs. 19) 5,487,129 m to three sig figs 20) 31,947.972 cm² to four sig figs 21) 192.6739 cm³ to five sig figs 22) 786.09164 cm to two sig figs 27) 35.27 cm to three sig figs 28) 1.35 m to two sig figs 29) 78,000,000 nm to four sig figs 30) 350.275 cm to three sig figs

Explanation:

Step1: Recall sig - fig 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. Trailing zeros in a whole number without a decimal point may or may not be significant, but when written in scientific notation, the significant figures are clear.

Step2: Determine sig - figs for 0.0120 m

Leading zeros are not significant. Non - zero digits 1 and 2 are significant, and the trailing zero after 2 is significant. So there are 3 sig - figs.

Step3: Determine sig - figs for 100.5 mL

Zeros between non - zero digits (the zero between 1 and 5) are significant. So there are 4 sig - figs.

Step4: Determine sig - figs for 350. cm²

The trailing zero after 5 with a decimal point is significant. So there are 3 sig - figs.

Step5: Determine sig - figs for 1000 kg

Without a decimal point, it's ambiguous. But if we assume it's measured to the nearest kg, it has 1 sig - fig.

Step6: Determine sig - figs for 0.0020700 dm

Leading zeros are not significant. Non - zero digits 2, 0, 7 are significant, and the two trailing zeros after 7 are significant. So there are 5 sig - figs.

Step7: Determine sig - figs for 0.000150 L

Leading zeros are not significant. Non - zero digits 1 and 5 are significant, and the trailing zero after 5 is significant. So there are 3 sig - figs.

Step8: Determine sig - figs for 998,870 cm³

Without a decimal point, it's ambiguous. If we assume it's measured to the nearest cm³, it has 5 sig - figs.

Step9: Determine sig - figs for 1.000×10⁴ kg

In scientific notation, all digits in the coefficient (1.000) are significant. So there are 4 sig - figs.

Step10: Determine sig - figs for 23,500 mg

Without a decimal point, it's ambiguous. If we assume it's measured to the nearest mg, it has 3 sig - figs.

Step11: Round 5,487,129 m to three sig - figs

First, identify the first three significant digits: 5, 4, 8. The next digit is 7 (≥ 5), so we round up. 5,487,129 ≈ 5.49×10⁶ m.

Step12: Round 31,947.972 cm² to four sig - figs

The first four significant digits are 3, 1, 9, 4. The next digit is 7 (≥ 5), so we round up. 31,947.972 ≈ 31,950 cm² (or 3.195×10⁴ cm²).

Step13: Round 192.6739 cm³ to five sig - figs

The first five significant digits are 1, 9, 2, 6, 7. The next digit is 3 (< 5), so we don't round up. 192.6739 ≈ 192.67 cm³.

Step14: Round 786.09164 cm to two sig - figs

The first two significant digits are 7, 8. The next digit is 6 (≥ 5), so we round up. 786.09164 ≈ 790 cm (or 7.9×10² cm).

Step15: Round 35.27 cm to three sig - figs

The first three significant digits are 3, 5, 2. The next digit is 7 (≥ 5), so we round up. 35.27 ≈ 35.3 cm.

Step16: Round 1.35 m to two sig - figs

The first two significant digits are 1, 3. The next digit is 5 (≥ 5), so we round up. 1.35 ≈ 1.4 m.

Step17: Round 78,000,000 nm to four sig - figs

In scientific notation, 78,000,000 = 7.800×10⁷ nm (we add two trailing zeros to get four significant digits).

Step18: Round 350.275 cm to three sig - figs

The first three significant digits are 3, 5, 0. The next digit is 2 (< 5), so we don't round up. 350.275 ≈ 350 cm (or 3.50×10² cm).

Answer:

1. 3
2. 4
3. 3
4. 1 (assuming measured to the nearest kg)
5. 5
6. 5.49×10⁶ m
7. 31,950 cm² (or 3.195×10⁴ cm²)
8. 192.67 cm³
9. 790 cm (or 7.9×10² cm)
10. 3
11. 5 (assuming measured to the nearest cm³)
12. 4
13. 3 (assuming measured to the nearest mg)
14. 35.3 cm
15. 1.4 m
16. 7.800×10⁷ nm
17. 350 cm (or 3.50×10² cm)