Question

calculating with significant figures homework
how many sig figs?
determine the number of sig figs for each of the following measurements.

1. 0.01400 m
2. 120.5 ml
3. 2500. cm²
4. 12000 kg
5. 0.0096700 dm

round the following measurements to the specified number of sig figs.

1. 5,475,204 m to six sig figs
2. 51,897.970 cm² to four sig figs
3. 200.6789 cm³ to five sig figs
4. 786,091,641 cm to two sig figs
5. 314.005 ml to 4 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.

Step2: Determine sig - figs for 0.01400 m

Leading zeros are not significant. Non - zero digits 1, 4 and trailing zeros after 4 are significant. So there are 4 sig - figs.

Step3: Determine sig - figs for 120.5 mL

All non - zero digits (1, 2, 5) and zero between non - zero digits are significant. So there are 4 sig - figs.

Step4: Determine sig - figs for 2500. cm²

The decimal point makes the trailing zeros significant. So there are 4 sig - figs.

Step5: Determine sig - figs for 12000 kg

Without a decimal point, the trailing zeros may or may not be significant. Assuming they are not significant for the sake of standard convention when no other information is given, there are 2 sig - figs.

Step6: Determine sig - figs for 0.0096700 dm

Leading zeros are not significant. Non - zero digits 9, 6, 7 and trailing zeros after 7 are significant. So there are 5 sig - figs.

Step7: Round 5475204 m to six sig - figs

The number is 5475204. To six sig - figs, we get 5475200 (we round down as the next digit is 4).

Step8: Round 51897.970 cm² to four sig - figs

The number is 51897.970. To four sig - figs, we look at the fifth digit. Since it is 7 (greater than 5), we round up. So we get 51900 (in scientific notation \(5.190\times 10^{4}\) to show 4 sig - figs more clearly).

Step9: Round 200.6789 cm³ to five sig - figs

The number is 200.6789. To five sig - figs, we get 200.68 (we round up as the next digit is 8).

Step10: Round 786091641 cm to two sig - figs

The number is 786091641. To two sig - figs, we look at the third digit. Since it is 6 (greater than 5), we round up. So we get 790000000 (in scientific notation \(7.9\times 10^{8}\)).

Step11: Round 314.005 mL to 4 sig - figs

The number is 314.005. To 4 sig - figs, we get 314.0 (we round down as the next digit is 0).

Answer:

1. 4
2. 4
3. 4
4. 2
5. 5
6. 5475200
7. 51900
8. 200.68
9. 790000000
10. 314.0