Operate on decimals and reason about place value.
Free, timed SHSAT practice sets on decimal arithmetic & place value— every question includes a full worked explanation, and there's no account required.
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Each operation has one rule for the decimal point.
Estimate first: \(0.64 \times 2.3\) is about 1.5, so \(14.72\) and \(0.1472\) are out.
Common traps: putting the point one place off, and writing \(0.\overline{36}\) as \(\frac{36}{100}\).
Line up the decimal points before combining: \(-20.4 - (-9.68) = -10.72\). Lining up \(-20.4\) one place off (as if it were \(-204\)) gives \(-194.32\). Adding instead of subtracting gives \(-30.08\). Lining up \(-9.68\) one place off (as if it were \(-96.8\)) gives \(76.4\).
Multiply the digits, then place the decimal point by counting total decimal places: \(0.73 \times 1.7 = 1.241\). Counting one decimal place too few gives \(12.41\). Counting one decimal place too many gives \(0.1241\). Counting two decimal places too many gives \(0.01241\).
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 \(\frac{1}{37}\).)