Convert Recurring Decimals to Fractions
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(0:01) How to Convert Recurring Decimals to Fractions: Start by setting the recurring decimal as ‘$x$’, then use multiplication to align the repeating parts, making subtraction possible to eliminate them.(0:10) Turn One-Digit Recurring Decimal to Fraction (Example): Let $x = 0.333\ldots$; multiply by 10 to get $10x = 3.333\ldots$ Subtract the equations to find $9x = 3$. So $x = \large \frac{1}{3}$.(0:46) Turn Two-Digit Recurring Decimal to Fraction (Example): Set $x = 0.4545\ldots$, multiply by 100 to get $100x = 45.4545\ldots$ Subtract the 2 equations to find $99x = 45$. So $x =\large \frac{5}{11}$.
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