Speed skill: convert instantly among common decimals, percents, and fractions on sight. Orthogonal fluency tag -- not a subtopic; may co-occur with ns/fraction-decimal-percent-equivalence or percents/percent-fraction-decimal-conversion.
A fluency sprint: build the speed and accuracy you need to do this calculation instantly on test day.
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To compare a mix of forms, change all of them to decimals, then compare place by place: \(\frac{7}{8} = 0.875\) and \(85\% = 0.85\), so \(\frac{7}{8}\) is bigger.
Common slips: moving the point only one place (\(7\% = 0.07\), not \(0.7\)), writing a repeating decimal over 10 or 100 as if it stops, and, in ratio questions, dividing a part by the other part instead of by the total (2 roses to 5 tulips means \(\frac{2}{7}\) of the flowers are roses).
A block of 2 repeating digits over 99: \(0.\overline{27} = \frac{27}{99} = \frac{3}{11}\). (Writing it as 0.27, as if the decimal stopped, gives \(\frac{27}{100}\). Putting 27 over 90 instead of 99 gives \(\frac{3}{10}\). Putting 27 over 999 instead of 99 gives \(\frac{1}{37}\).)
\(0.7\) is 70%, so the clearance value is 70% of \(\$288.00\), which is \(\$201.60\). (Moving the decimal point the wrong way (using \(7\) instead of \(0.7\)) gives $2016.00. Reading \(0.7\) as 7% instead of 70% gives $20.16. Finding the value NOT on clearance (\(1 - 0.7 = 0.3\) of the stock) gives $86.40.)
Total balls \(= 5 + 3 = 8\). Percent that are basketballs \(= (5 \div 8) \times 100 = 62.5\%\). (Dividing by 3 (the other part) instead of the total 8 gives the wrong answer about 166.67%. Finding the percent that are soccer balls instead gives 37.5%. Forgetting to multiply by 100 gives about 0.63%.)