Fraction Classroom
Decimal explanations

Grade 5 · Read, model and practise

Divide by ten without losing a placeholder

Make each place-value unit one tenth as large and keep any empty places needed to record it.

Try the practice questions

Start with this question

What happens when 3.6 is divided into ten equal shares?

The key idea: Each share is 0.36. Three ones become three tenths per share, and six tenths become six hundredths per share.

Make the idea visible

The second row is one tenth of the first. No nonzero digit is discarded.OnesTenthsHundredthsThousandths36000360
The second row is one tenth of the first. No nonzero digit is discarded.
  1. Read 3.6 as three ones and six tenths. Keep both contributions visible.
  2. Divide each contribution by ten: three ones become three tenths, and six tenths become six hundredths.
  3. Write 0.36 and multiply it by ten to recover 3.6. The zero before the point names zero whole units.
  4. When the result has an empty tenths place, record a zero there too. For example, 0.4 ÷ 10 = 0.04.

A useful error to discuss

A learner might say: Remove a zero or erase a digit when dividing by ten.

Division changes the size of the quantity; it does not delete information. Track each digit as its unit becomes one tenth as large.

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

0.48 · Four ones become four tenths; eight tenths become eight hundredths.

Practice 2

Answer & reasoning

0.07 · Seven tenths become seven hundredths.

Practice 3

Answer & reasoning

0.06 · Six hundredths is 6/100.

Independent check

Answer & reasoning

0.008 · Eight hundredths become eight thousandths.

Explain a new situation

How can multiplication check the result of 2.5 ÷ 100?

Discuss the explanation

The result is 0.025. Multiplying 0.025 by 100 gives 2.5, recovering the starting amount.

Materials for your group

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Choose the next step

If a nonzero digit disappears, reconstruct the starting quantity with multiplication. If secure, alternate multiplication and division by powers of ten.

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Original Fraction Classroom examples and explanations. Curriculum reference: CCSS 5.NBT.A.2. Grade alignment describes the intended topic; it is not an endorsement or evidence of classroom results.

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