Recognize, match, and ORDER equivalent forms among fractions, decimals (incl. repeating), and percents. Use for identify/compare/order questions where the equivalence itself is the point (not as a step inside a percent computation -- see percents/percent-fraction-decimal-conversion).
Free, timed SHSAT practice sets on fraction/decimal/percent equivalence & ordering— every question includes a full worked explanation, and there's no account required.
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To compare numbers in different forms, change them all to decimals.
To order a list, write every value with the same number of decimal places, then compare. For \(\frac{12}{20}\), \(\frac{5}{8}\), \(14\%\) and \(0.71\): \(0.600\), \(0.625\), \(0.140\), \(0.710\). The greatest is \(0.71\).
Learn these benchmarks: \(\frac{1}{8} = 0.125\), \(\frac{1}{5} = 0.2\), \(\frac{1}{4} = 0.25\), \(\frac{1}{3} = 0.\overline{3}\), \(\frac{3}{8} = 0.375\).
Common traps: moving the point three places (\(87.5\% \ne 0.0875\)), forgetting to move it (\(87.5\% \ne 87.5\)), and thinking a bigger denominator means a bigger fraction.
Divide the percent by 100: \(37.5\% = 37.5 \div 100 = 0.375\). Forgetting to divide by 100 gives \(37.5\). Dividing by 1000 instead of 100 gives \(0.0375\). Dividing 100 by 37.5 instead of 37.5 by 100 gives about \(2.6667\).
Convert every value to a decimal to compare: \(\frac{2}{20} = 0.1\), \(\frac{39}{50} = 0.78\), \(9\% = 0.09\), and \(0.42\). The least value is \(9\%\).
\(\frac{1}{4} = 0.25 = 25\%\), and \(\frac{2}{8}\) reduces to \(\frac{1}{4}\). \(\frac{1}{2} = 0.5\) and \(0.025 = 2.5\%\) are not equal to \(\frac{1}{4}\).