Year 5: Per cent
Part of the Year 5 decimals and percentages chapter. Chapter overview · whole chapter on one page
Per cent
The symbol % means per cent, which is “out of one hundred”. The square below has 100 small squares, and 35 of them are shaded. So 35% of the square is shaded.
A percentage can be written three ways: as a fraction with denominator 100, as a decimal, and with the % sign. For example, 35% = 35/100 = 0.35. In its simplest form, 35/100 is 7/20.
Key ideas
- Per cent means out of 100. 35% = 35/100.
- A percentage as a decimal: divide by 100, which moves the digits two places to the right. 7% = 0.07.
- A decimal as a percentage: multiply by 100, which moves the digits two places to the left. 0.8 = 80%.
- Simplify the fraction if you can: 35/100 = 7/20.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 35% means 35 out of 100, so write it over 100.35⁄100
- Simplify the fraction. The HCF of 35 and 100 is 5. Divide the top and the bottom by 5.35⁄100 = 7⁄20
- Write the answer. This fraction is in its simplest form.7⁄20
Check. 7⁄20 is the same as 35 out of 100. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.8 = 80⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.8 × 100 = 80
- Write the answer. 80%
Check. 80% = 80⁄100 = 0.8. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 7% means 7 out of 100, so write it over 100.7⁄100
- Divide by 100. Dividing by 100 moves every digit two places to the right, so the answer is a decimal.7 ÷ 100 = 0.07
- Write the answer. 0.07
Check. 0.07 × 100 = 7, so 0.07 is 7%. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Watch out
7% is 0.07, not 0.7. Per cent means hundredths, so the 7 is in the hundredths column. 0.7 is 70%.Exercise 7E Per cent as fractions and decimals
Non-calculatorKey words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 27% means 27 out of 100, so write it over 100.27⁄100
- Write the answer. This fraction is in its simplest form.27⁄100
Check. 27⁄100 is the same as 27 out of 100. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 9% means 9 out of 100, so write it over 100.9⁄100
- Write the answer. This fraction is in its simplest form.9⁄100
Check. 9⁄100 is the same as 9 out of 100. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 50% means 50 out of 100, so write it over 100.50⁄100
- Simplify the fraction. The HCF of 50 and 100 is 50. Divide the top and the bottom by 50.50⁄100 = 1⁄2
- Write the answer. This fraction is in its simplest form.1⁄2
Check. 1⁄2 is the same as 50 out of 100. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 100% means 100 out of 100, so write it over 100.100⁄100
- Simplify the fraction. The HCF of 100 and 100 is 100. Divide the top and the bottom by 100.100⁄100 = 1⁄1
- Write the answer. This fraction is in its simplest form.1
Check. 1 is the same as 100 out of 100. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 45% means 45 out of 100, so write it over 100.45⁄100
- Simplify the fraction. The HCF of 45 and 100 is 5. Divide the top and the bottom by 5.45⁄100 = 9⁄20
- Divide by 100. Dividing by 100 moves every digit two places to the right, so the answer is a decimal.45 ÷ 100 = 0.45
- Write the answer. 0.45
Check. 0.45 × 100 = 45, so 0.45 is 45%. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 6% means 6 out of 100, so write it over 100.6⁄100
- Simplify the fraction. The HCF of 6 and 100 is 2. Divide the top and the bottom by 2.6⁄100 = 3⁄50
- Divide by 100. Dividing by 100 moves every digit two places to the right, so the answer is a decimal.6 ÷ 100 = 0.06
- Write the answer. 0.06
Check. 0.06 × 100 = 6, so 0.06 is 6%. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 100% means 100 out of 100, so write it over 100.100⁄100
- Simplify the fraction. The HCF of 100 and 100 is 100. Divide the top and the bottom by 100.100⁄100 = 1⁄1
- Divide by 100. Dividing by 100 moves every digit two places to the right, so the answer is a decimal.100 ÷ 100 = 1
- Write the answer. 1
Check. 1 × 100 = 100, so 1 is 100%. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of one hundred. Write the percentage over 100, then change it to the form you need.
- Per cent means out of 100. 3% means 3 out of 100, so write it over 100.3⁄100
- Divide by 100. Dividing by 100 moves every digit two places to the right, so the answer is a decimal.3 ÷ 100 = 0.03
- Write the answer. 0.03
Check. 0.03 × 100 = 3, so 0.03 is 3%. ✓
Watch out. Per cent means per hundred, so 7% is 7 hundredths: 0.07, not 0.7.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.72 = 72⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.72 × 100 = 72
- Write the answer. 72%
Check. 72% = 72⁄100 = 0.72. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.9 = 90⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.9 × 100 = 90
- Write the answer. 90%
Check. 90% = 90⁄100 = 0.9. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.05 = 5⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.05 × 100 = 5
- Write the answer. 5%
Check. 5% = 5⁄100 = 0.05. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.4 = 40⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.4 × 100 = 40
- Write the answer. 40%
Check. 40% = 40⁄100 = 0.4. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Out of 100 means per cent. The number out of 100 is the percentage.
- Per cent means out of 100. The question tells us the amount out of 100, so the number is the percentage.40 out of 100 = 40⁄100
- Write the answer with the % sign. The % sign shows the answer is per cent.40%
Check. 40% = 40⁄100 = 0.4. ✓
Watch out. Check that the total really is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Out of 100 means per cent. The number out of 100 is the percentage.
- Per cent means out of 100. The question tells us the amount out of 100, so the number is the percentage.65 out of 100 = 65⁄100
- Write the answer with the % sign. The % sign shows the answer is per cent.65%
Check. 65% = 65⁄100 = 0.65. ✓
Watch out. Check that the total really is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Out of 100 means per cent. The number out of 100 is the percentage.
- Per cent means out of 100. The question tells us the amount out of 100, so the number is the percentage.8 out of 100 = 8⁄100
- Write the answer with the % sign. The % sign shows the answer is per cent.8%
Check. 8% = 8⁄100 = 0.08. ✓
Watch out. Check that the total really is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Write both values as percentages, then compare them.
- Write 0.55 as a percentage. 0.55 has two decimal places, so it is 55 hundredths.0.55 = 55⁄100 = 55%
- Compare the two percentages. The larger percentage is the larger amount.60% > 55%
- Write the answer. 60% is greater.
Check. 60% = 0.6, and 0.6 is more than 0.55. ✓
Watch out. Compare like with like. Change both to percentages or both to decimals first.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Per cent means out of 100, so the top number is the percentage.
- Write 14% over 100. The % sign means out of 100.14% = 14⁄100
- Read the top number. The top number is 14.14
Check. 14 out of 100 is 14%. ✓
Watch out. Write the number with no % sign.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.61 = 61⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.61 × 100 = 61
- Write the answer. 61%
Check. 61% = 61⁄100 = 0.61. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Out of 100 means per cent. The number out of 100 is the percentage.
- Per cent means out of 100. The question tells us the amount out of 100, so the number is the percentage.62 out of 100 = 62⁄100
- Write the answer with the % sign. The % sign shows the answer is per cent.62%
Check. 62% = 62⁄100 = 0.62. ✓
Watch out. Check that the total really is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Out of 100 means per cent. The number out of 100 is the percentage.
- Per cent means out of 100. The question tells us the amount out of 100, so the number is the percentage.84 out of 100 = 84⁄100
- Write the answer with the % sign. The % sign shows the answer is per cent.84%
Check. 84% = 84⁄100 = 0.84. ✓
Watch out. Check that the total really is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Find the sweets that are not red first, then write the number out of 100 as a percentage.
- Find the number that is not red. There are 100 sweets altogether. Take away the 9 red ones.100 − 9 = 91
- Write it out of 100. The bag has 100 sweets, so 91 out of 100 is 91%.91 out of 100 = 91⁄100
- Write the answer. 91%
Check. 9% are red and 9 + 91 = 100. ✓
Watch out. Check that the total is 100 before you read the number as a percentage.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change the decimal to hundredths. The number of hundredths is the percentage.
- Write the decimal as hundredths. Hundredths are the same as per cent: 1 hundredth = 1%.0.2 = 20⁄100
- Read the number of hundredths as the percentage. Multiplying by 100 moves the digits two places to the left.0.2 × 100 = 20
- Write the answer. 20%
Check. 20% = 20⁄100 = 0.2. ✓
Watch out. Multiplying by 100 moves the digits two places to the LEFT. Dividing by 100 moves them two places to the right.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Write 7% as a decimal and compare it with 0.7.
- Write 7% as hundredths. Per cent means hundredths, so 7% = 7 hundredths.7% = 7⁄100
- Write it as a decimal. Seven hundredths has its 7 in the second decimal place.7⁄100 = 0.07
- Compare. 0.7 = 70%, which is ten times bigger than 7%.0.07 ≠ 0.7
- Write the answer. No. 7% = 0.07.
Check. 0.07 × 100 = 7. ✓
Watch out. Per cent is out of 100. A decimal with one place is tenths, not hundredths.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Change all three to percentages, then compare them.
- Change each one to a percentage. Use the method that fits each number.
Number As a percentage 0.5 50% 45% 45% 4/10 40% - Compare the percentages. The biggest percentage is the greatest number.50% > 45% > 40%
- Write the answer. 0.5 is the greatest.
Check. 0.5 = 50%, 45% and 4/10 = 40%. ✓
Watch out. Change all the numbers to the same form before you compare them.
Key words. Per cent means “out of one hundred”. The symbol % shows per cent: 35% means 35 out of 100, which is 35 hundredths.
Method. Write 1% as a fraction and as a decimal, then look for a pattern.
- Write 1% as a fraction. Per cent means out of 100, so 1% = 1 out of 100.1% = 1⁄100
- Write 1% as a decimal. One hundredth is 0.01.1⁄100 = 0.01
- Write the answer. The fraction and the decimal are both one hundredth.1⁄100 = 0.01
Check. 0.01 × 100 = 1. ✓
Watch out. Each step of 1% is one place value in a decimal: 1% = 0.01.