Rounding too early sprint

Round intermediate values, producing a distractor-matching final answer.

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

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How to avoid rounding too early

In a sample, 14 of 30 students walk to school. About how many of 1,500 students walk? If you round \(14 \div 30 \approx 0.47\) up to 0.5 first, you get \(0.5 \times 1500 = 750\). The exact answer is \(\tfrac{14}{30} \times 1500 = 700\). One early rounding made the answer off by 50.

Students round early because long decimals feel messy. But the error grows when you multiply by a big number, and the test often puts that wrong number in the choices.

Check habits:

Worked examples

Example 1.
In a random sample of 30 commuters, 26 said they take the bus. Based on this sample, about how many of the 1110 commuters in the full population would be expected to say the same?
Show answer and explanation
Answer:
C

Sample proportion = 26 \(\div\) 30. Apply it to the full population: 26 \(\div\) 30 \(\times\) 1110 = 962. (Adding the difference instead of scaling (\(26 + (1110 - 30)\)) gives 1106. Rounding 26 \(\div\) 30 to 0.9 before multiplying (\(0.9 \times 1110\)) gives 999. Stopping at the scale factor (\(1110 \div 30\)) gives 37.)

Example 2.
What is the exact value of \(47 \times 39\)?
Show answer and explanation
Answer:
C

Multiply the exact values: \(47 \times 39 = 1833\). Rounding both numbers to the nearest ten first (50 and 40) gives \(2000\). Rounding only 47 (to 50) gives \(1950\). Rounding only 39 (to 40) gives \(1880\).

Example 3.
In a random sample of 60 commuters, 21 said they take the bus. Based on this sample, about how many of the 600 commuters in the full population would be expected to say the same?
Show answer and explanation
Answer:
A

Sample proportion = 21 \(\div\) 60. Apply it to the full population: 21 \(\div\) 60 \(\times\) 600 = 210. (Adding the difference instead of scaling (\(21 + (600 - 60)\)) gives 561. Rounding 21 \(\div\) 60 to 0.4 before multiplying (\(0.4 \times 600\)) gives 240. Stopping at the scale factor (\(600 \div 60\)) gives 10.)