Fraction Classroom
Decimal explanations

Grade 4 · Read, model and practise

Compare decimals when their lengths differ

Compare the first different place instead of treating the digits after the point as a whole number.

Try the practice questions

Start with this question

Which is greater, 0.8 or 0.75?

The key idea: 0.8 is greater. Eight tenths is eighty hundredths, and eighty hundredths is greater than seventy-five hundredths.

Make the idea visible

The wholes match. A longer written decimal does not necessarily represent a larger number.0.80: 80 hundredths0.75: 75 hundredths
The wholes match. A longer written decimal does not necessarily represent a larger number.
  1. Check that both decimals describe the same whole and the same measurement unit.
  2. Compare ones first, then tenths. Both numbers have zero ones; 0.8 has eight tenths, while 0.75 has seven tenths and five hundredths.
  3. Rename 0.8 as 0.80 if a common unit helps. Compare 80 hundredths and 75 hundredths.
  4. Record 0.8 > 0.75 and explain the first place that settled the comparison. If the tenths are equal, compare hundredths next.

A useful error to discuss

A learner might say: 75 is greater than 8, so 0.75 must be greater than 0.8.

The two digit strings are counting different units. Rename both quantities in hundredths or compare the tenths first.

Practise, then check

Try the first three questions with the model. Try the final check without help. A correct value is a starting point: explain how your units or drawing support it.

Practice 1

Answer & reasoning

> · 60 hundredths is greater than 58 hundredths.

Practice 2

Answer & reasoning

< · The tenths match; two hundredths is less than nine hundredths.

Practice 3

Answer & reasoning

= · Four tenths is forty hundredths.

Independent check

Answer & reasoning

< · One tenth is ten hundredths, just above nine hundredths.

Explain a new situation

Can you decide whether 0.9 or 0.86 is greater without rewriting either number?

Discuss the explanation

Yes. Compare tenths: nine tenths is greater than eight tenths plus six hundredths, which is still below nine tenths.

Materials for your group

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Choose the next step

If the learner compares 86 with 9, return to equal wholes and hundredths. If secure, ask for a number lying between two decimals.

Open a related complete lesson →

Original Fraction Classroom examples and explanations. Curriculum reference: CCSS 4.NF.C.7. Grade alignment describes the intended topic; it is not an endorsement or evidence of classroom results.

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