Year 6: Per cent, fractions and decimals
Part of the Year 6 percentages chapter. Chapter overview · whole chapter on one page
Per cent, fractions and decimals
A percentage is a fraction with 100 as the bottom number. The word comes from per cent, which means out of 100. If 35 squares of a 100 square are shaded, then 35 out of 100 are shaded: that is 35%.
A percentage, a decimal and a fraction can all name the same amount. 35% is 35/100, which is 0.35. Once you know these equivalences, you can change between the three forms quickly.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 2/5 | 0.4 | 40% |
| 3/5 | 0.6 | 60% |
| 4/5 | 0.8 | 80% |
| 1/10 | 0.1 | 10% |
| 1/20 | 0.05 | 5% |
| 1/25 | 0.04 | 4% |
| 1/8 | 0.125 | 12.5% |
| 3/8 | 0.375 | 37.5% |
Learn these pairs. Each one is worth knowing well.
Key ideas
- Per cent means out of 100. The sign % shows it.
- To change a percentage to a decimal, divide by 100 (move the point two places left): 35% = 0.35.
- To change a decimal to a percentage, multiply by 100 (move the point two places right): 0.7 = 70%.
- To change a fraction to a percentage, make the bottom number 100 or divide, then multiply by 100: 3/8 = 37.5%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.35
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.35 × 100 = 35
- Write the answer as a percentage. So the decimal is this many out of 100.35
Check. 35% ÷ 100 = 0.35. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.3 ÷ 8 = 0.375
- Multiply the decimal by 100. That turns the decimal into per cent.0.375 × 100 = 37.5
- Write the answer. 37.5
Check. 37.5% ÷ 100 = 0.375, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Write 60% out of 100, then simplify the fraction.
- Write the percentage as a fraction out of 100. Per cent means out of 100.60% = 60/100
- Find the highest common factor (HCF) of the top and the bottom. It is the biggest number that divides into both.HCF of 60 and 100 is 20
- Divide the top and the bottom by the HCF. This makes the fraction as simple as possible.60 ÷ 20 = 3, and 100 ÷ 20 = 5
- Write the answer. 3/5
Check. 3/5 as a percentage is 60%. ✓
Watch out. Simplify by dividing the top and the bottom by the same number, not by taking away.
Watch out
0.4 is 40%, not 4%. Many pupils move the point the wrong way. 4% is 0.04, which is a tenth of 0.4.
Exam tip
Grown-up tip. Ask: “Out of 100, how many?” Most questions become easy once the bottom number is 100.
Exercise 6A Fractions, decimals and percentages
Non-calculatorKey words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Write 50% out of 100, then simplify the fraction.
- Write the percentage as a fraction out of 100. Per cent means out of 100.50% = 50/100
- Find the highest common factor (HCF) of the top and the bottom. It is the biggest number that divides into both.HCF of 50 and 100 is 50
- Divide the top and the bottom by the HCF. This makes the fraction as simple as possible.50 ÷ 50 = 1, and 100 ÷ 50 = 2
- Write the answer. 1/2
Check. 1/2 as a percentage is 50%. ✓
Watch out. Simplify by dividing the top and the bottom by the same number, not by taking away.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Write 20% out of 100, then simplify the fraction.
- Write the percentage as a fraction out of 100. Per cent means out of 100.20% = 20/100
- Find the highest common factor (HCF) of the top and the bottom. It is the biggest number that divides into both.HCF of 20 and 100 is 20
- Divide the top and the bottom by the HCF. This makes the fraction as simple as possible.20 ÷ 20 = 1, and 100 ÷ 20 = 5
- Write the answer. 1/5
Check. 1/5 as a percentage is 20%. ✓
Watch out. Simplify by dividing the top and the bottom by the same number, not by taking away.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Write 75% out of 100, then simplify the fraction.
- Write the percentage as a fraction out of 100. Per cent means out of 100.75% = 75/100
- Find the highest common factor (HCF) of the top and the bottom. It is the biggest number that divides into both.HCF of 75 and 100 is 25
- Divide the top and the bottom by the HCF. This makes the fraction as simple as possible.75 ÷ 25 = 3, and 100 ÷ 25 = 4
- Write the answer. 3/4
Check. 3/4 as a percentage is 75%. ✓
Watch out. Simplify by dividing the top and the bottom by the same number, not by taking away.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Write 40% out of 100, then simplify the fraction.
- Write the percentage as a fraction out of 100. Per cent means out of 100.40% = 40/100
- Find the highest common factor (HCF) of the top and the bottom. It is the biggest number that divides into both.HCF of 40 and 100 is 20
- Divide the top and the bottom by the HCF. This makes the fraction as simple as possible.40 ÷ 20 = 2, and 100 ÷ 20 = 5
- Write the answer. 2/5
Check. 2/5 as a percentage is 40%. ✓
Watch out. Simplify by dividing the top and the bottom by the same number, not by taking away.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Divide the percentage by 100 to get a decimal.
- Write the percentage as a fraction out of 100. Per cent means out of 100.60% = 60/100
- Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.60 ÷ 100 = 0.6
- Write the answer. Use a zero to hold a place if one is needed.0.6
Check. 0.6 × 100 = 60, so the decimal is 60%. ✓
Watch out. 60% is not 60. Divide by 100 first; 5% is 0.05, not 0.5.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Divide the percentage by 100 to get a decimal.
- Write the percentage as a fraction out of 100. Per cent means out of 100.5% = 5/100
- Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.5 ÷ 100 = 0.05
- Write the answer. Use a zero to hold a place if one is needed.0.05
Check. 0.05 × 100 = 5, so the decimal is 5%. ✓
Watch out. 5% is not 5. Divide by 100 first; 5% is 0.05, not 0.5.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Divide the percentage by 100 to get a decimal.
- Write the percentage as a fraction out of 100. Per cent means out of 100.35% = 35/100
- Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.35 ÷ 100 = 0.35
- Write the answer. Use a zero to hold a place if one is needed.0.35
Check. 0.35 × 100 = 35, so the decimal is 35%. ✓
Watch out. 35% is not 35. Divide by 100 first; 5% is 0.05, not 0.5.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Divide the percentage by 100 to get a decimal.
- Write the percentage as a fraction out of 100. Per cent means out of 100.8% = 8/100
- Divide by 100: move the decimal point two places to the left. Dividing by 100 makes the number 100 times smaller.8 ÷ 100 = 0.08
- Write the answer. Use a zero to hold a place if one is needed.0.08
Check. 0.08 × 100 = 8, so the decimal is 8%. ✓
Watch out. 8% is not 8. Divide by 100 first; 5% is 0.05, not 0.5.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.7
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.7 × 100 = 70
- Write the answer as a percentage. So the decimal is this many out of 100.70
Check. 70% ÷ 100 = 0.7. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.45
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.45 × 100 = 45
- Write the answer as a percentage. So the decimal is this many out of 100.45
Check. 45% ÷ 100 = 0.45. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.03
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.03 × 100 = 3
- Write the answer as a percentage. So the decimal is this many out of 100.3
Check. 3% ÷ 100 = 0.03. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.125
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.125 × 100 = 12.5
- Write the answer as a percentage. So the decimal is this many out of 100.12.5
Check. 12.5% ÷ 100 = 0.125. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 20.
- Make the bottom number 100. 5 × 20 = 100, so multiply the top and the bottom by 20.3/5 = 60/100
- Read the top number as per cent. Out of 100 means per cent.60/100 = 60%
- Write the answer. 60
Check. 60% ÷ 100 = 0.6, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 5.
- Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.7/20 = 35/100
- Read the top number as per cent. Out of 100 means per cent.35/100 = 35%
- Write the answer. 35
Check. 35% ÷ 100 = 0.35, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 4.
- Make the bottom number 100. 25 × 4 = 100, so multiply the top and the bottom by 4.9/25 = 36/100
- Read the top number as per cent. Out of 100 means per cent.36/100 = 36%
- Write the answer. 36
Check. 36% ÷ 100 = 0.36, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.1 ÷ 8 = 0.125
- Multiply the decimal by 100. That turns the decimal into per cent.0.125 × 100 = 12.5
- Write the answer. 12.5
Check. 12.5% ÷ 100 = 0.125, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change the fraction to a decimal, then multiply it by 100.
- Divide the top number by the bottom number. A fraction bar means divide.3 ÷ 8 = 0.375
- Multiply the decimal by 100. That turns the decimal into per cent.0.375 × 100 = 37.5
- Write the answer. 37.5
Check. 37.5% ÷ 100 = 0.375, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Change each number to a decimal or to a percentage, then compare.
- Write 4/10 as a decimal. Divide 4 by 10.4/10 = 0.4
- Write 40% as a decimal. 40 out of 100 is 40/100.40% = 0.4
- Write 4% and 0.04 as decimals. 4% is 4/100, which is 0.04.4% = 0.04, and 0.04 is not 0.4
- Write 2/5 as a decimal. Divide 2 by 5.2/5 = 0.4
- Write the answer. Three numbers are equal to 0.4.4/10, 40%, 2/5
Check. 0.4 = 4/10 = 40% = 2/5. ✓
Watch out. 4% and 0.04 look like 40% and 0.4, but they are ten times smaller.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Write every number as a decimal, then put the decimals in order.
- Write each number as a decimal. Percentages become decimals by dividing by 100.0.3, 35% = 0.35, 1/4 = 0.25, 0.22
- Order the decimals, smallest first. Compare the tenths, then the hundredths.0.22 < 0.25 < 0.3 < 0.35
- Write the answer in the original forms. Keep each number as it was written.0.22, 1/4, 0.3, 35%
Check. 0.22 is 22%, 1/4 is 25%, 0.3 is 30% and 35% is 35%. ✓
Watch out. Do not compare 35 with 3 and 22 by their digits. Put them all into the same form first.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Change 1/8 to a decimal, then to a percentage, and compare with 18%.
- Write 1/8 as a decimal. 1 ÷ 8 = 0.125.1 ÷ 8 = 0.125
- Write 0.125 as a percentage. Multiply by 100.0.125 × 100 = 12.5
- Compare with 18%. 12.5% is not the same as 18%.12.5% ≠ 18%
- Write the answer. No. 1/8 = 0.125 = 12.5%.
Check. 1/8 is one eighth, which is a little more than 1/10 (10%). ✓
Watch out. 1/8 is a little more than 10%, not nearly 20%.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 10.
- Make the bottom number 100. 10 × 10 = 100, so multiply the top and the bottom by 10.1/10 = 10/100
- Read the top number as per cent. Out of 100 means per cent.10/100 = 10%
- Write the answer. 10
Check. 10% ÷ 100 = 0.1, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 5.
- Make the bottom number 100. 20 × 5 = 100, so multiply the top and the bottom by 5.1/20 = 5/100
- Read the top number as per cent. Out of 100 means per cent.5/100 = 5%
- Write the answer. 5
Check. 5% ÷ 100 = 0.05, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 4.
- Make the bottom number 100. 25 × 4 = 100, so multiply the top and the bottom by 4.1/25 = 4/100
- Read the top number as per cent. Out of 100 means per cent.4/100 = 4%
- Write the answer. 4
Check. 4% ÷ 100 = 0.04, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Make the bottom number 100 by multiplying by 2.
- Make the bottom number 100. 50 × 2 = 100, so multiply the top and the bottom by 2.3/50 = 6/100
- Read the top number as per cent. Out of 100 means per cent.6/100 = 6%
- Write the answer. 6
Check. 6% ÷ 100 = 0.06, which is the same as the fraction we started with. ✓
Watch out. Multiply by 100 at the end, not at the start.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Write the decimal over 100, then simplify the fraction.
- Write the decimal as a fraction out of 100. Hundredths go over 100. 0.80 is 80 hundredths.0.80 = 80/100
- Find the highest common factor of the top and the bottom. It is the biggest number that divides into both.HCF of 80 and 100 is 20
- Divide the top and the bottom by the HCF. This makes the fraction simpler.80 ÷ 20 = 4, 100 ÷ 20 = 5
- Write the answer. 4/5
Check. 4/5 = 0.8. ✓
Watch out. Read 0.04 as 4 hundredths, not as 4 tenths.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Write the decimal over 100, then simplify the fraction.
- Write the decimal as a fraction out of 100. Hundredths go over 100. 0.04 is 4 hundredths.0.04 = 4/100
- Find the highest common factor of the top and the bottom. It is the biggest number that divides into both.HCF of 4 and 100 is 4
- Divide the top and the bottom by the HCF. This makes the fraction simpler.4 ÷ 4 = 1, 100 ÷ 4 = 25
- Write the answer. 1/25
Check. 1/25 = 0.04. ✓
Watch out. Read 0.04 as 4 hundredths, not as 4 tenths.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Write the decimal over 100, then simplify the fraction.
- Write the decimal as a fraction out of 100. Hundredths go over 100. 0.75 is 75 hundredths.0.75 = 75/100
- Find the highest common factor of the top and the bottom. It is the biggest number that divides into both.HCF of 75 and 100 is 25
- Divide the top and the bottom by the HCF. This makes the fraction simpler.75 ÷ 25 = 3, 100 ÷ 25 = 4
- Write the answer. 3/4
Check. 3/4 = 0.75. ✓
Watch out. Read 0.04 as 4 hundredths, not as 4 tenths.
Key words. Per cent means out of 100. The sign % means per cent, so 35% means 35 out of 100. It can be written as the fraction 35/100 or the decimal 0.35.
Method. Multiply the decimal by 100. The answer is the number of per cent.
- Write the decimal. Read the decimal carefully, with its point.0.125
- Multiply by 100: move the decimal point two places to the right. Multiplying by 100 gives the number of hundredths, which is per cent.0.125 × 100 = 12.5
- Write the answer as a percentage. So the decimal is this many out of 100.12.5
Check. 12.5% ÷ 100 = 0.125. ✓
Watch out. Do not forget the step. 0.7 is 70%, not 7%.
Key words. Equivalent means the same value. 1/2, 0.5 and 50% are equivalent: three ways of writing one amount.
Method. Compare the two numbers in the same form.
- Write 3/8 as a decimal. 3 divided by 8.3/8 = 0.375
- Write 0.375 as a percentage. Multiply by 100.0.375 × 100 = 37.5
- Compare with 37%. 37.5% is more than 37%, so 37% is not the same.37.5% ≠ 37%
- Write the answer. No. 3/8 = 0.375 = 37.5%, not 37%.
Check. 37% = 0.37, which is less than 0.375. ✓
Watch out. Look at the hundredths: 0.37 and 0.375 are different.