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$Convert the decimal below to a fraction in simplest form. 0.864 Answer:$

Convert the decimal below to a fraction in simplest form. $\newline$ $0.864$ $\newline$ Answer:

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Convert between decimals and fractions

Full solution

Q. Convert the decimal below to a fraction in simplest form.

\newline

0.864

\newline

Answer:

Write Decimal as Fraction: Write the decimal as a fraction with a denominator of $1$ . $0.864$ can be written as $\frac{0.864}{1}$ .
Multiply by Power of $10$ : Multiply the numerator and denominator by a power of $10$ to eliminate the decimal places. $\newline$ Since there are three decimal places, multiply both the numerator and denominator by $1000$ to get $\frac{864}{1000}$ . $\newline$ $\frac{864}{1000} = \frac{(0.864 \times 1000)}{(1 \times 1000)}$
Find GCD and Simplify: Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator. $\newline$ The GCD of $864$ and $1000$ is $8$ .
Divide by GCD: Divide both the numerator and the denominator by the GCD to simplify the fraction. $\newline$ $864 \div 8 = 108$ $\newline$ $1000 \div 8 = 125$ $\newline$ So, $\frac{864}{1000}$ simplifies to $\frac{108}{125}$ .

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