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Express 0.24 as a fraction.

April 25, 2026Mathematics

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Answer

-0.6199

6 steps

Express 0.24 as a fraction.
$0.24 = \frac{24}{100}$
Apply the logarithm quotient rule, $\log \left(\frac{a}{b}\right) = \log a - \log b$ .
$\log_{10} 0.24 = \log_{10} \left(\frac{24}{100}\right) = \log_{10} 24 - \log_{10} 100$
Factorize 24 into its prime factors and simplify $\log_{10} 100$ .
$24 = 2^3 \times 3$ $\log_{10} 100 = \log_{10} 10^2 = 2 \log_{10} 10 = 2 \times 1 = 2$
Substitute these into the expression.
$\log_{10} 0.24 = \log_{10} (2^3 \times 3) - 2$
Apply the logarithm product rule, $\log (ab) = \log a + \log b$ , and the power rule, $\log (a^n) = n \log a$ .
$\log_{10} (2^3 \times 3) - 2 = \log_{10} (2^3) + \log_{10} 3 - 2$ $= 3 \log_{10} 2 + \log_{10} 3 - 2$
Substitute the given values $\log_{10} 2 = 0.3010$ and $\log_{10} 3 = 0.4771$ .
$= 3(0.3010) + 0.4771 - 2$ $= 0.9030 + 0.4771 - 2$ $= 1.3801 - 2$ $= -0.6199$
The value of $\log_{10} 0.24$ is:
$-0.6199$

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