Fraction Classroom
Decimal explanations

Grade 4 · Read, model and practise

Why are 0.6 and 0.60 equal?

Repartition tenths into hundredths without changing the whole or the shaded amount.

Try the practice questions

Start with this question

Does writing 0.60 instead of 0.6 make the amount larger?

The key idea: No. Six tenths and sixty hundredths describe the same share of the same whole.

Make the idea visible

Each outlined bar is one whole. The shaded portions end at the same place.0.6 = 6/100.60 = 60/100
Each outlined bar is one whole. The shaded portions end at the same place.
  1. Shade six parts of a whole divided into ten equal parts. Leave the four unshaded tenths visible.
  2. Split every tenth into ten equal pieces, including the unshaded parts. The whole now contains one hundred equal pieces.
  3. The six shaded tenths contain sixty hundredths. The shaded endpoint and the reference whole have not moved.
  4. Write 6/10 = 60/100, then 0.6 = 0.60. A final zero can extend the notation without changing value; a zero inserted before the 6 would move it to another place.

A useful error to discuss

A learner might say: The number with more digits must be larger.

Count the unit as well as the digits. Sixty hundredths uses ten times as many pieces, but each piece is one tenth as large as a tenth.

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

70 · Seven tenths contains seventy hundredths.

Practice 2

Answer & reasoning

= · Both represent three tenths.

Practice 3

Answer & reasoning

0.40 · Forty hundredths can be written 0.40 or 0.4.

Independent check

Answer & reasoning

< · Five hundredths is less than fifty hundredths. This zero is a placeholder, not a final zero.

Explain a new situation

Explain how ten tenths can also be called one hundred hundredths.

Discuss the explanation

Each of the ten tenths contains ten hundredths, so the same whole contains 10 × 10 = 100 hundredths.

Materials for your group

Student pages and teacher answers are separate. Download an HTML file to keep or use your browser to print or save as PDF.

Print student pagesPrint teacher answers

Choose the next step

If the learner counts pieces without naming their size, align the two wholes and compare endpoints. Then move to decimal comparisons.

Open a related complete lesson →

Original Fraction Classroom examples and explanations. Curriculum reference: CCSS 4.NF.C.5. Grade alignment describes the intended topic; it is not an endorsement or evidence of classroom results.

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