Decimal place shift sprint

Misplace the decimal point in place-value or scientific-notation problems.

An error-pattern drill: practice spotting and avoiding this specific SHSAT trap.

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How to avoid putting the decimal point in the wrong place

What is \(0.2 \times 0.3\)? Many students write 0.6. The right answer is 0.06. Each factor has one decimal place, so the product needs \(1 + 1 = 2\) decimal places.

One wrong place changes the answer by a factor of 10, and the test puts that number in the choices. The digits are right, so the answer looks right.

Check habits:

Worked examples

Example 1.
What is \(27.5 + 8.99\)?
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Answer:
C

Line up the decimal points before combining: \(27.5 + 8.99 = 36.49\). Lining up \(27.5\) one place off (as if it were \(275\)) gives \(283.99\). Subtracting instead of adding gives \(18.51\). Lining up \(8.99\) one place off (as if it were \(89.9\)) gives \(117.4\).

Example 2.
A winter coat costs \(\$83.00\). What is 25% of that price?
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Answer:
C

25% of \(\$83.00\) \(= 25/100 \times 83 = \$20.75\). (Dividing by 10 instead of 100 (\(83 \times 25 \div 10\)) gives $207.50. Finding the price after taking 25% off (\(\$83.00 - \$20.75\)) gives $62.25. Dividing by 1000 instead of 100 gives about $2.08.) 25% of the price is $20.75.

Example 3.
What is \(8.4 \times 10^{-2}\) written in standard form?
Show answer and explanation
Answer:
D

Move the decimal point 2 places left: \(8.4 \times 10^{-2} = 0.084\). Moving the decimal point one place too many gives \(0.0084\). Moving the decimal point one place too few gives \(0.84\). Moving the decimal point 2 places right instead gives \(840\).