Convert between percentages fractions and decimals

What you will learn

• Convert between percentages fractions and decimals

Models used: number sentences, stories, diagrams.

Before you start

• Percentage means per hundred

Percent is a share of one hundred

This grid is one whole. It has 100 equal squares.

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

   This grid is one whole. It has 100 equal squares.

   25% is 25 out of 100, which is 25/100 and 0.25.

   0/100 = 0 = 0%

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

   Shade 25 squares. We have shaded one quarter of the whole.

   25 out of 100 = 25%

   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.

   25/100 = 0.25 = 25%

3. The full bar represents $80, which is 100%. The shaded share is 25%.

   Now the whole is $80. One quarter of $80 is $20.

   25% of $80 = $20

   Each section: 5% = $4

   0%100% = $80

   25% of $80 = $20

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

   The fraction, decimal and percentage describe the same share.

   1/4 = 0.25 = 25%

   80

   20one quarter60three quarters

Worked example: A new example, together

75 of 100 equal squares are shaded. What percentage is shaded?

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

   Write the percentage over a hundred first, then simplify it or read it as a decimal.

   Percentages, fractions and decimals can name the same part of a whole.

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

   Percent means 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.

   75 of 100 equal squares are shaded. What percentage is shaded?

   75 %

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

   Percent means 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.

   75/100 = 0.75 = 75%

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

   75% = 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%

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

   This is 3/4 as a fraction, or 0.75 as a decimal.

   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%

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

   Check the result against the question we started with.

   0.75 × 100 = 75%.

   We found 75 %. Percentages, fractions and decimals can name the same part of a whole.

   75/100 = 0.75 = 75%

Common mistakes to discuss

• Moving the point the wrong way. Per cent means out of a hundred. 25% is 25/100, which is 0.25, not 2.5.

Check your understanding

• Convert between percentages fractions and decimals
• move between a percentage, a fraction and a decimal
• 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.