Express the following decimals in the form (p)/(q). 0.003overline (52)

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Express the following decimals in the form (p)/(q). 0.003overline (52)

Answer 1

<div class="c2h-answers">Let, $x=0.003 \overline{52}$ Obviously, there are three digits on the right side of the decimal point that have no bars.So, first we need to multiply both sides. $x$ by $10^{3}$ In this way, there are only repeated decimals left on the right side of the decimal point. $1000 x=3 . \overline{52}$ $1000 x=3+0.52$ $1000 x=3+\frac{52}{99}$ $1000 x=\frac{3 \times 99+52}{99}$ $1000 x=\frac{297+52}{99}$ $1000 x=\frac{349}{99}$ $x=\frac{349}{99000}$ Therefore, the decimal form of the given number is. $x=\frac{349}{99000}$.

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Express the following decimals in the form (p)/(q). 0.003overline (52)

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