Find the error: comparing decimals

A find-the-error worksheet for which is greater, 0.45 or 0.5? The two classic decimal misconceptions. Each problem shows a student's worked solution with one planted mistake; students find the wrong step, name the misconception and solve it correctly. The answer key is computed, so it is always right.

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Mistakes this sheet plants

Thought more digits means a bigger number. Comparing the digits after the point as whole numbers ignores place value. Write both with the same number of decimal places first.Example: Which is greater: 0.7 or 0.351? worked to 0.351 instead of 0.7.
Thought tenths always beat hundredths. A number with only tenths is not automatically bigger. Write both with the same number of decimal places, then compare.Example: Which is greater: 0.4 or 0.45? worked to 0.4 instead of 0.45.

Grade 4 · 4.NF.C.7, 5.NBT.A.3b

Find the error: comparing decimals

Name Date

Each problem was solved by a student, and each has exactly one mistake. Find the step with the mistake, say what went wrong, and solve the problem correctly.

1 Which is greater: 0.4 or 0.45?

Maya's work
1. 0.4 is in tenths and 0.45 is in hundredths. Tenths are bigger than hundredths.
2. So 0.4 is greater.
Maya's answer: 0.4

Wrong step: What went wrong: Correct answer:
2 Which is greater: 0.7 or 0.351?

Jade's work
1. Compare the digits after the decimal point: 351 is more than 7.
2. So 0.351 is greater.
Jade's answer: 0.351

Wrong step: What went wrong: Correct answer:
3 Which is greater: 0.15 or 0.1?

Max's work
1. 0.1 is in tenths and 0.15 is in hundredths. Tenths are bigger than hundredths.
2. So 0.1 is greater.
Max's answer: 0.1

Wrong step: What went wrong: Correct answer:
4 Which is greater: 0.499 or 0.7?

Kai's work
1. Compare the digits after the decimal point: 499 is more than 7.
2. So 0.499 is greater.
Kai's answer: 0.499

Wrong step: What went wrong: Correct answer:

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Answer key · Grade 4 · 4.NF.C.7, 5.NBT.A.3b

Find the error: comparing decimals

#	Wrong step	The mistake	Correct answer
1	Step 1	Thought tenths always beat hundredths. A number with only tenths is not automatically bigger. Write both with the same number of decimal places, then compare.Correct step 1: Write both with 2 decimal places: 0.40 and 0.45.	0.45not 0.4
2	Step 1	Thought more digits means a bigger number. Comparing the digits after the point as whole numbers ignores place value. Write both with the same number of decimal places first.Correct step 1: Write both with 3 decimal places: 0.700 and 0.351.	0.7not 0.351
3	Step 1	Thought tenths always beat hundredths. A number with only tenths is not automatically bigger. Write both with the same number of decimal places, then compare.Correct step 1: Write both with 2 decimal places: 0.15 and 0.10.	0.15not 0.1
4	Step 1	Thought more digits means a bigger number. Comparing the digits after the point as whole numbers ignores place value. Write both with the same number of decimal places first.Correct step 1: Write both with 3 decimal places: 0.499 and 0.700.	0.7not 0.499

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