Chapter 2: Problem 32

Perform the following operation. Express the answer in scientific notation and with the correct number of significant figures. $$\frac{\left(6.12433 \times 10^{6} \mathrm{m}^{3}\right)}{\left(7.15 \times 10^{-3}\mathrm{m}\right)}$$

Short Answer

Expert verified

The result is $8.56x10^8 m^2$.

Step by step solution

Division of Numbers

First, separate the numbers from the powers of ten and divide them. This gives\[\frac{{6.12433}}{{7.15}}\]

Division of Powers of Ten

Next, divide the powers of ten. According to the rule of division of exponents, subtract the exponent in the denominator from the exponent in the numerator. \[\frac{{10^{6}}}{{10^{-3}}}\]becomes\[10^{6-(-3)} = 10^9\]

Calculate Final Results

The division of the numbers provides approximately 0.85623 and the division of the powers of ten gives $10^9$. Multiply these two results to get the final figure before adjustments for significant numbers.

Adjust for Significant Figures

Express the result to the correct number of significant figures. The least significant figures given in the question is 3 (from 7.15), so adjust the final result to 3 significant figures: 0.856x10^9.

Express in Scientific Notation

The result must be expressed in scientific notation, whereby the part before the ‘x’ must be between 1 and 10. Adjust by increasing the power of ten: $8.56x10^8 m^2$.

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Perform the following operation. Express the answer in scientific notation and with the correct number of significant figures. $$\frac{\left(6.12433 \times 10^{6} \mathrm{m}^{3}\right)}{\left(7.15 \times 10^{-3}\mathrm{m}\right)}$$

Short Answer

Step by step solution

Division of Numbers

Division of Powers of Ten

Calculate Final Results

Adjust for Significant Figures

Express in Scientific Notation

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