Convert fractions to decimals

What you will learn

• Convert fractions to decimals

Models used: number sentences, stories, tables.

Before you start

• Express a whole-number division as a fraction

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

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

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 69/100 as a decimal.

1. A fraction is a quotient. Read each value with the heading above its column.

   Keep the amount fixed as its parts are renamed. Check which place names each decimal digit.

   A fraction is the numerator divided by the denominator.

   A fraction is a quotient

   Fraction	Division
   69/100	69 ÷ 100

2. A fraction is a quotient. Read each value with the heading above its column.

   The fraction means 69 ÷ 100.

   A fraction is a quotient

   Fraction	Division
   69/100	69 ÷ 100

   Write 69/100 as a decimal.

   0.69

3. A fraction is a quotient. Read each value with the heading above its column.

   Use equivalent hundredths where possible: 69/100 = 69/100.

   A fraction is a quotient

   Fraction	Division
   69/100	69 ÷ 100

4. A fraction is a quotient. Read each value with the heading above its column.

   69 hundredths = 0.69.

   A fraction is a quotient

   Fraction	Division
   69/100	69 ÷ 100

5. A fraction is a quotient. Read each value with the heading above its column.

   Check the result against the question we started with.

   0.69 × 100 = 69.

   We found 0.69. A fraction is the numerator divided by the denominator.

   A fraction is a quotient

   Fraction	Division
   69/100	69 ÷ 100

Common mistakes to discuss

• Reading the fraction as digits. A fraction is a division, not a pair of digits. 1/4 is 0.25, not 0.14.

Check your understanding

• Convert fractions to decimals
• connect fraction notation with decimal place value
• 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.