Question

how many significant figures are contained in each of the following measurements?
2×10^18 m
9.74150×10^-4 j
0.0613 cm^3
4.500.000
9.740×10^4 m/s

Explanation:

Step1: Identify significant - figure rules

Non - zero digits are always significant.

Step2: Analyze \(2\times10^{18}\ m\)

The number 2 is a non - zero digit. So, it has 1 significant figure.

Step3: Analyze \(9.74150\times10^{-4}\ J\)

Non - zero digits and trailing zeros after a decimal point are significant. So, it has 6 significant figures.

Step4: Analyze \(0.0613\ cm^{3}\)

Leading zeros are not significant. Non - zero digits are significant. So, it has 3 significant figures.

Step5: Analyze \(4500000\)

If there is no decimal point, trailing zeros may or may not be significant. Assuming no additional information, we consider non - zero digits significant. So, it has 3 significant figures.

Step6: Analyze \(9.740\times10^{4}\ m/s\)

Non - zero digits and the trailing zero after the decimal point are significant. So, it has 4 significant figures.

Answer:

1. \(2\times10^{18}\ m\): one
2. \(9.74150\times10^{-4}\ J\): six
3. \(0.0613\ cm^{3}\): three
4. \(4500000\): three
5. \(9.740\times10^{4}\ m/s\): four