Convert fractions to decimals when the denominator is a factor of 10 or 100

What you will learn

• Convert fractions to decimals when the denominator is a factor of 10 or 100

Models used: number sentences, stories, fraction strips.

Before you start

• Tenths, hundredths and thousandths

Rename the fraction in tenths or hundredths

How can we write three quarters as a decimal?

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Three of four equal pieces are shaded. This is three quarters of the whole.

   3/4

   Tenths, hundredths and thousandths name equal parts of a whole. These names let us write the same amount as a fraction.

2. The grid is the same whole, cut into one hundred equal pieces.

   Each quarter is 25 hundredths. Three quarters therefore cover 75 of the hundred small squares.

   3/4 = 75/100

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   75/100 = 0.75 = 75%

3. Read the place heading before the digit. A counter in a different column has a different value.

   Seventy-five hundredths means seven tenths and five more hundredths. Write 0.75.

   75/100 = 0.75

   Ones0

   Tenths7

   Hundredths5

   0.75 = 7 tenths + 5 hundredths

4. The whole grid has 100 equal squares. One full row is 10 hundredths, or one tenth.

   We have changed the name, not the amount: the fraction and decimal describe the same shaded share.

   3/4 = 0.75

   One small square is one hundredth of the whole. Ten small squares make one tenth, so the same shaded amount can be described in more than one way.

   75/100 = 0.75 = 75%

Worked example: A new example, together

Write 32/50 as a decimal.

1. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Keep the chosen amount unchanged while naming its place-value units.

   Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

2. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   The fraction means 32 ÷ 50.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

   Write 32/50 as a decimal.

   0.64

3. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   The fraction means 32 ÷ 50.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

4. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Rename it in hundredths: 64/100.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

5. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   32/50 = 0.64.

   The size of a fraction depends on both numbers: how many equal parts make the whole, and how many of those parts we take.

6. Each strip is one whole of the same size. Count all the equal parts, then count the shaded parts.

   Check the result against the question we started with.

   Undo the operation to recover the starting quantity.

   We found 0.64. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

Common mistakes to discuss

• Writing the digits of the fraction. Make an equivalent fraction in tenths or hundredths first. 3/4 = 75/100 = 0.75, not 0.34.

Check your understanding

• Convert fractions to decimals when the denominator is a factor of 10 or 100
• connect decimals and fractions through equal-sized units
• check the answer against the original quantities and units

Explain your reasoning to an adult, then try a fresh question in the interactive lesson. A result from one attempt is not proof of lasting mastery.