Express decimals as fractions

What you will learn

• Express decimals as fractions

Models used: number sentences, stories, diagrams.

Before you start

• Divide whole numbers with a decimal quotient and round the result

Read the last decimal place to name the fraction

How can we write 0.35 as a fraction?

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

   The last digit is in the hundredths column. So 0.35 means thirty-five hundredths.

   0.35 = 35/100

   Ones0

   Tenths3

   Hundredths5

   0.35 = 3 tenths + 5 hundredths

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

   Shade 35 squares of a hundred-square whole. This shows why the denominator is one hundred.

   35 shaded parts out of 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.

   35/100 = 0.35 = 35%

3. The complete bar is the whole. Each labelled section is one part of it.

   If we simplify, divide both numbers by five. Seven groups of five shaded squares are out of twenty groups of five.

   35/100 = 7/20

   100

   55555555555555555555

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

   Both fractions describe the same amount. Simplifying changes the size and count of parts together.

   0.35 = 35/100 = 7/20

   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.

   35/100 = 0.35 = 35%

Worked example: A new example, together

Write 0.9 as a fraction in simplest form.

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

   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.

   Ones0

   Tenths9

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

   The fraction means 18 ÷ 20.

   Ones0

   Tenths9
   Write 0.9 as a fraction in simplest form.

   9/10

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

   Rename it in hundredths: 90/100.

   Ones0

   Tenths9

   0.9 = 9 tenths

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

   18/20 = 0.9.

   Ones0

   Tenths9

   0.9 = 9 tenths

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

   Check the result against the question we started with.

   Undo the operation to recover the starting quantity.

   We found 9/10. Each decimal column names a unit ten times smaller than the one before it. Matching those units keeps the value clear.

   Ones0

   Tenths9

   0.9 = 9 tenths

Common mistakes to discuss

• Using the wrong denominator. The last digit names the denominator. 0.07 is 7/100, while 0.7 is 7/10.

Check your understanding

• Express decimals as fractions
• 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.