GCSE Maths: Percentages, fractions and decimals (Foundation)

Method. Count the shaded squares. The whole grid has 100 squares.

1. Count the shaded squares. Count in rows of 10 to be quick.
   37 squares are shaded.
2. Write it out of 100. There are 100 squares in total.
   37100

Check. 37 + 63 = 100, so the unshaded squares make up the rest. ✓

Method. A percentage is the number of parts out of 100.

1. Use the fraction out of 100. The top number of a fraction out of 100 is the percentage.
   37100 = 37%
2. Write the answer.
   37%

Check. 37% of the grid is 37 squares out of 100. ✓

Method. Divide the percentage by 100 to get the decimal.

1. Write the percentage.
   37%
2. Divide by 100. The digits move two places to the right.
   37 ÷ 100 = 0.37

Check. 0.37 × 100 = 37. ✓

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   8% = 8100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   8 ÷ 100 = 0.08
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   8% = 0.08

Check. Go back the other way: 0.08 × 100 = 8, which is 8%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   45% = 45100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   45 ÷ 100 = 0.45
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   45% = 0.45

Check. Go back the other way: 0.45 × 100 = 45, which is 45%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   70% = 70100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   70 ÷ 100 = 0.7
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   70% = 0.7

Check. Go back the other way: 0.7 × 100 = 70, which is 70%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   3% = 3100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   3 ÷ 100 = 0.03
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   3% = 0.03

Check. Go back the other way: 0.03 × 100 = 3, which is 3%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   125% = 125100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   125 ÷ 100 = 1.25
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   125% = 1.25

Check. Go back the other way: 1.25 × 100 = 125, which is 125%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. A percentage is a number out of 100, so to change it to a decimal divide by 100 (move every digit two places to the right of the decimal point).

1. Write the percentage as a number over 100. Per cent means “out of 100”.
   12.5% = 12.5100
2. Divide by 100. Dividing by 100 moves each digit two places to the right in the place-value table (the decimal point moves two places left).
   12.5 ÷ 100 = 0.125
3. Check the size. A percentage below 100% must give a decimal below 1, and a small percentage a small decimal.
   12.5% = 0.125

Check. Go back the other way: 0.125 × 100 = 12.5, which is 12.5%. ✓

Watch out. The decimal point moves two places, not one. 5% is 0.05, not 0.5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   50% = 50100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 50: 1, 2, 5, 10, 25, 50
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 50.
3. Divide the top and the bottom by 50. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   50 ÷ 50 = 1 and 100 ÷ 50 = 2
   50100 = 12

Check. As a decimal, 50% = 0.5 and 12 = 0.5. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   20% = 20100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 20: 1, 2, 4, 5, 10, 20
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 20.
3. Divide the top and the bottom by 20. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   20 ÷ 20 = 1 and 100 ÷ 20 = 5
   20100 = 15

Check. As a decimal, 20% = 0.2 and 15 = 0.2. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   15% = 15100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 15: 1, 3, 5, 15
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 5.
3. Divide the top and the bottom by 5. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   15 ÷ 5 = 3 and 100 ÷ 5 = 20
   15100 = 320

Check. As a decimal, 15% = 0.15 and 320 = 0.15. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   45% = 45100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 45: 1, 3, 5, 9, 15, 45
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 5.
3. Divide the top and the bottom by 5. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   45 ÷ 5 = 9 and 100 ÷ 5 = 20
   45100 = 920

Check. As a decimal, 45% = 0.45 and 920 = 0.45. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   4% = 4100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 4: 1, 2, 4
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 4.
3. Divide the top and the bottom by 4. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   4 ÷ 4 = 1 and 100 ÷ 4 = 25
   4100 = 125

Check. As a decimal, 4% = 0.04 and 125 = 0.04. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. Write the percentage as a fraction out of 100, then simplify by dividing the top and the bottom by their highest common factor.

1. Write the percentage as a fraction out of 100. Per cent means “out of 100”.
   85% = 85100
2. List the factors of the top and the bottom. We want the biggest number that divides into both. This is the highest common factor (HCF).
   Factors of 85: 1, 5, 17, 85
   Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
   The highest common factor is 5.
3. Divide the top and the bottom by 5. Dividing both by the same number does not change the value of the fraction, but it makes the numbers smaller.
   85 ÷ 5 = 17 and 100 ÷ 5 = 20
   85100 = 1720

Check. As a decimal, 85% = 0.85 and 1720 = 0.85. ✓

Watch out. Always simplify. 40% = 40/100 is not finished until you reach 2/5.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   0.27 × 100 = 27
2. Write the % sign. The answer is now a number out of 100.
   0.27 = 27%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   0.27 is less than 1, so 27% is less than 100%.

Check. Divide back: 27 ÷ 100 = 0.27. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   0.9 × 100 = 90
2. Write the % sign. The answer is now a number out of 100.
   0.9 = 90%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   0.9 is less than 1, so 90% is less than 100%.

Check. Divide back: 90 ÷ 100 = 0.9. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   0.05 × 100 = 5
2. Write the % sign. The answer is now a number out of 100.
   0.05 = 5%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   0.05 is less than 1, so 5% is less than 100%.

Check. Divide back: 5 ÷ 100 = 0.05. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   0.375 × 100 = 37.5
2. Write the % sign. The answer is now a number out of 100.
   0.375 = 37.5%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   0.375 is less than 1, so 37.5% is less than 100%.

Check. Divide back: 37.5 ÷ 100 = 0.375. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   1.2 × 100 = 120
2. Write the % sign. The answer is now a number out of 100.
   1.2 = 120%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   1.2 is more than 1, so 120% is more than 100%.

Check. Divide back: 120 ÷ 100 = 1.2. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a decimal to a percentage, multiply by 100.

1. Multiply the decimal by 100. A percentage is a number out of 100, so we scale the decimal up by 100 (move each digit two places to the left).
   2.5 × 100 = 250
2. Write the % sign. The answer is now a number out of 100.
   2.5 = 250%
3. Check the size. A decimal below 1 is less than 100%, and a decimal above 1 is more than 100%.
   2.5 is more than 1, so 250% is more than 100%.

Check. Divide back: 250 ÷ 100 = 2.5. ✓

Watch out. Do not just add a % sign. 0.6 is 60%, not 0.6%.

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   12
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 2 × 50 = 100.
   12 = 50100 = 50%

Check. 50% = 50 ÷ 100 = 0.5, and 1 ÷ 2 = 0.5. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   14
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 4 × 25 = 100.
   14 = 25100 = 25%

Check. 25% = 25 ÷ 100 = 0.25, and 1 ÷ 4 = 0.25. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   34
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 4 × 25 = 100.
   34 = 75100 = 75%

Check. 75% = 75 ÷ 100 = 0.75, and 3 ÷ 4 = 0.75. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   110
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 10 × 10 = 100.
   110 = 10100 = 10%

Check. 10% = 10 ÷ 100 = 0.1, and 1 ÷ 10 = 0.1. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   15
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 5 × 20 = 100.
   15 = 20100 = 20%

Check. 20% = 20 ÷ 100 = 0.2, and 1 ÷ 5 = 0.2. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   25
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 5 × 20 = 100.
   25 = 40100 = 40%

Check. 40% = 40 ÷ 100 = 0.4, and 2 ÷ 5 = 0.4. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   710
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 10 × 10 = 100.
   710 = 70100 = 70%

Check. 70% = 70 ÷ 100 = 0.7, and 7 ÷ 10 = 0.7. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   925
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 25 × 4 = 100.
   925 = 36100 = 36%

Check. 36% = 36 ÷ 100 = 0.36, and 9 ÷ 25 = 0.36. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   320
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 20 × 5 = 100.
   320 = 15100 = 15%

Check. 15% = 15 ÷ 100 = 0.15, and 3 ÷ 20 = 0.15. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   1750
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 50 × 2 = 100.
   1750 = 34100 = 34%

Check. 34% = 34 ÷ 100 = 0.34, and 17 ÷ 50 = 0.34. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   1120
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 20 × 5 = 100.
   1120 = 55100 = 55%

Check. 55% = 55 ÷ 100 = 0.55, and 11 ÷ 20 = 0.55. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   1325
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 25 × 4 = 100.
   1325 = 52100 = 52%

Check. 52% = 52 ÷ 100 = 0.52, and 13 ÷ 25 = 0.52. ✓

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   38
2. Divide the top by the bottom. This changes the fraction into a decimal.
   3 ÷ 8 = 0.375
3. Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.
   0.375 × 100 = 37.5%

Check. 37.5% = 37.5 ÷ 100 = 0.375, and 3 ÷ 8 = 0.375. ✓

Watch out. Percentages are out of 100. A fraction like 3/8 cannot be written over 100 directly, so divide instead.

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   58
2. Divide the top by the bottom. This changes the fraction into a decimal.
   5 ÷ 8 = 0.625
3. Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.
   0.625 × 100 = 62.5%

Check. 62.5% = 62.5 ÷ 100 = 0.625, and 5 ÷ 8 = 0.625. ✓

Watch out. Percentages are out of 100. A fraction like 3/8 cannot be written over 100 directly, so divide instead.

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   740
2. Divide the top by the bottom. This changes the fraction into a decimal.
   7 ÷ 40 = 0.175
3. Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.
   0.175 × 100 = 17.5%

Check. 17.5% = 17.5 ÷ 100 = 0.175, and 7 ÷ 40 = 0.175. ✓

Watch out. Percentages are out of 100. A fraction like 3/8 cannot be written over 100 directly, so divide instead.

Method. To change a fraction to a percentage, find an equivalent fraction with denominator 100, or divide the top by the bottom and multiply by 100.

1. Write the fraction. A fraction already compares a part with a whole.
   916
2. Divide the top by the bottom. This changes the fraction into a decimal.
   9 ÷ 16 = 0.5625
3. Multiply by 100. To change a decimal into a percentage multiply by 100, because a percentage is a number out of 100.
   0.5625 × 100 = 56.25%

Check. 56.25% = 56.25 ÷ 100 = 0.5625, and 9 ÷ 16 = 0.5625. ✓

Watch out. Percentages are out of 100. A fraction like 3/8 cannot be written over 100 directly, so divide instead.

Method. Divide the top by the bottom to get the decimal. Multiply the decimal by 100 to get the percentage.

1. Divide the numerator by the denominator. A fraction bar means “divide”. This gives the decimal.
   3 ÷ 5 = 0.6
2. Multiply the decimal by 100. A percentage is a number out of 100.
   0.6 × 100 = 60
3. Write the answer.
   35 = 0.6 = 60%

Check. 60% = 60100 = 35. ✓

Method. Divide the top by the bottom to get the decimal. Multiply the decimal by 100 to get the percentage.

1. Divide the numerator by the denominator. A fraction bar means “divide”. This gives the decimal.
   7 ÷ 20 = 0.35
2. Multiply the decimal by 100. A percentage is a number out of 100.
   0.35 × 100 = 35
3. Write the answer.
   720 = 0.35 = 35%

Check. 35% = 35100 = 720. ✓

Method. Divide the top by the bottom to get the decimal. Multiply the decimal by 100 to get the percentage.

1. Divide the numerator by the denominator. A fraction bar means “divide”. This gives the decimal.
   17 ÷ 25 = 0.68
2. Multiply the decimal by 100. A percentage is a number out of 100.
   0.68 × 100 = 68
3. Write the answer.
   1725 = 0.68 = 68%

Check. 68% = 68100 = 1725. ✓

Method. Divide the top by the bottom to get the decimal. Multiply the decimal by 100 to get the percentage.

1. Divide the numerator by the denominator. A fraction bar means “divide”. This gives the decimal.
   1 ÷ 8 = 0.125
2. Multiply the decimal by 100. A percentage is a number out of 100.
   0.125 × 100 = 12.5
3. Write the answer.
   18 = 0.125 = 12.5%

Check. 12.5% = 12.5100 = 18. ✓

Method. To compare fractions, decimals and percentages, write them all as decimals. Then put the decimals in order.

1. Change every number into a decimal. Decimals are easy to compare digit by digit, so we use them as a common language.
   35 = 3 ÷ 5 = 0.6
   0.55 is already a decimal: 0.55
   62% = 62 ÷ 100 = 0.62
2. Put the decimals in order. We want smallest first. Compare the digits from the left, starting with the tenths.
   0.55 , 0.6 , 0.62
3. Write the original numbers in that order. The answer should use the forms given in the question.
   0.55 ,  35 ,  62%

Check. Read the final list again as decimals: it goes up each time. ✓

Watch out. Do not compare the digits of different forms directly. 3/5 is not smaller than 0.4 just because 3 is smaller than 4.

Method. To compare fractions, decimals and percentages, write them all as decimals. Then put the decimals in order.

1. Change every number into a decimal. Decimals are easy to compare digit by digit, so we use them as a common language.
   0.4 is already a decimal: 0.4
   720 = 7 ÷ 20 = 0.35
   36% = 36 ÷ 100 = 0.36
2. Put the decimals in order. We want smallest first. Compare the digits from the left, starting with the tenths.
   0.35 , 0.36 , 0.4
3. Write the original numbers in that order. The answer should use the forms given in the question.
   720 ,  36% ,  0.4

Check. Read the final list again as decimals: it goes up each time. ✓

Watch out. Do not compare the digits of different forms directly. 3/5 is not smaller than 0.4 just because 3 is smaller than 4.

Method. To compare fractions, decimals and percentages, write them all as decimals. Then put the decimals in order.

1. Change every number into a decimal. Decimals are easy to compare digit by digit, so we use them as a common language.
   45% = 45 ÷ 100 = 0.45
   920 = 9 ÷ 20 = 0.45
   0.405 is already a decimal: 0.405
   25 = 2 ÷ 5 = 0.4
2. Put the decimals in order. We want smallest first. Compare the digits from the left, starting with the tenths.
   0.4 , 0.405 , 0.45 , 0.45
3. Write the original numbers in that order. The answer should use the forms given in the question.
   25 ,  0.405 ,  45% ,  920

Check. Read the final list again as decimals: it goes up each time. ✓

Watch out. Do not compare the digits of different forms directly. 3/5 is not smaller than 0.4 just because 3 is smaller than 4.

Method. To write one quantity as a percentage of another: write it as a fraction (part over whole), then change the fraction into a percentage.

1. Write the part over the whole as a fraction. A percentage compares a part with the whole. Both numbers must be in the same units.
   1825
2. Make the denominator 100. “Per cent” means out of 100. Multiply the top and the bottom by the same number: 25 × 4 = 100.
   1825 = 72100 = 72%

Check. Check: 72% of 25 = 0.72 × 25 = 18, which is the part we started with. ✓

Watch out. Divide by the whole (the amount you are comparing with), not by the part.

Method. Subtract from 100%, or work out the number who do not walk.

1. Find how many do not walk. The class has 25 students and 18 walk.
   25 − 18 = 7
2. Write 7 out of 25 as a percentage. Multiply top and bottom by 4 to make the denominator 100.
   725 = 28100 = 28%

Check. 72% + 28% = 100%. ✓

Watch out. The two percentages must add up to 100%.