Understand and Apply the Conversion of Fractions, Decimals and Percentages 3 Worksheet

Fantastic work! You have decided to spend some time practising for the SATs Maths tests.

This activity is going to focus on practising your ability to convert between decimal numbers, fractions and percentages.

You will also be asked to complete worded problems involving these types of conversions.

Fractions, decimal numbers and percentages are just three ways of saying the same thing.

1⁄2 = 0.5 = 50%

Fractions, decimals and percentages all represent parts of a whole.

All three of these Maths terms look quite different but don't worry, this activity is a great way for you to learn about the relationship between them.

How do we convert a fraction to a decimal number?

To convert a fraction to a decimal number, we divide its numerator (top number) by its denominator (bottom number).

The line separating a fraction has the same meaning as the ÷ sign.

1⁄2 = 1 ÷ 2= 0.5

3⁄4 = 3 ÷ 4 = 0.75

Remember to use the bus stop method of division to help you solve the sum.

How do we convert between decimal numbers and percentages?

To convert a decimal number to a percentage, we multiply the decimal number by 100.

Remember, when you multiply by 100, move all of the digits two places to the left.

0.75 x 100% = 75.0% = 75%

Look at the place value chart below to see the movement of the digits.

Hundreds	Tens	Ones	.	Tenths	Hundredths
		0	.	7	5
	7	5	.	0

To convert a percentage to a decimal number, we divide the decimal number by 100.

Remember, when you divide by 100, move all of the digits two places to the right.

75% ÷ 100 = 0.75

Look at the place value chart below to see the movement of the digits.

Hundreds	Tens	Ones	.	Tenths	Hundredths
	7	5	.	0
		0	.	7	5

Over to you now to have a go at some practice questions...good luck!

Convert this fraction to a decimal number:

5⁄8

Convert this decimal number to a percentage:

0.35

Convert this percentage to a decimal number:

72%

Andy ate 10% of a cake, Tom ate the rest.

How much of the cake did Tom eat as a decimal number?

0.65

0.8

0.9

0.95

James ate 25% of a cake, Stuart ate the rest.

How much of the cake did Stuart eat as a decimal number?

Anna and Zara share a chocolate bar.

Annie eats 4⁄10 of the bar.

How much does Zara eat as a percentage?

60%

70%

75%

65%

Rob and Pete share a chocolate bar.

Rob eats 2⁄10 of the bar.

How much does Pete eat as a percentage?

There are 20 balls in a bag.

0.75 of them are red.

How many are blue as a percentage?

marbles

20%

25%

30%

28%

In a packet of 200 stickers, 3⁄4 are gold. The rest are silver.

Which decimal number represents the number of silver stickers?

0.2

0.25

0.1

0.28

In a packet of 300 stickers, 1⁄2 are gold. The rest are silver.

Which decimal number represents the number of silver stickers?

0.3

0.4

0.6

0.5

ANSWERS

Question 1

Convert this fraction to a decimal number:

5⁄8

CORRECT ANSWER

0.625

EDDIE SAYS

How did you get on with this first question? Hopefully, you remembered that to convert a fraction to a decimal, we have to divide the numerator by the denominator. Remember, you can use the bus stop division method to help you with this tricky type of division.

ANSWERS

Question 2

Convert this decimal number to a percentage:

0.35

CORRECT ANSWER

35%

EDDIE SAYS

Did you manage to work out that 0.35 as a percentage is 35%? Remember to convert a decimal number to a percentage, we multiply by 100 and move each digit 2 places to the left. Use a place value chart if it helps you.

ANSWERS

Question 3

Convert this percentage to a decimal number:

72%

CORRECT ANSWER

0.72

EDDIE SAYS

Great job if you chose 0.72. To convert a percentage to a decimal number, we need to divide by 100. This involves moving all of the digits 2 places to the right.

ANSWERS

Question 4

Andy ate 10% of a cake, Tom ate the rest.

How much of the cake did Tom eat as a decimal number?

CORRECT ANSWER

0.9

EDDIE SAYS

How are you doing? The best way to solve this type of question is to first find the answer as a percentage as that is the unit you have been given. Tom ate the rest of the cake, which means he ate 90% as Andy only ate 10%. The whole cake is worth 100%. Then to convert a percentage to a decimal, we have to divide 90 by 100 which gives us the answer of 0.9

ANSWERS

Question 5

James ate 25% of a cake, Stuart ate the rest.

How much of the cake did Stuart eat as a decimal number?

CORRECT ANSWER

0.75

EDDIE SAYS

Great job if you wrote 0.75. This question required the same steps of working out as the previous one. Remember to work in percentages first and then convert to a decimal number. You are making super progress and are halfway through the activity, keep it up!

ANSWERS

Question 6

Anna and Zara share a chocolate bar.

Annie eats 4⁄10 of the bar.

How much does Zara eat as a percentage?

CORRECT ANSWER

60%

EDDIE SAYS

Did you spot that Zara ate 60% of the chocolate bar? Again, the best way to work through this type of worded problem is to start by using the given unit. We know that Annie ate 4⁄10 of the chocolate bar, which means Zara must have eaten 6⁄10. 10⁄10 is the same as the whole chocolate bar. However, remember to finish the question by converting this to a percentage! To convert a fraction to a percentage, we must divide the numerator by the denominator and then multiply by 100. This gives us the answer 60%.

ANSWERS

Question 7

Rob and Pete share a chocolate bar.

Rob eats 2⁄10 of the bar.

How much does Pete eat as a percentage?

CORRECT ANSWER

80%

EDDIE SAYS

Don't panic if you found that tricky, practice makes perfect! If Rob ate 2⁄10 of the chocolate bar, Pete ate 8⁄10 of the bar. When 8⁄10 is converted to a percentage, it becomes 80%. This is brilliant progress- keep going, you are well over halfway through the activity!

ANSWERS

Question 8

There are 20 balls in a bag.

0.75 of them are red.

How many are blue as a percentage?

marbles

CORRECT ANSWER

25%

EDDIE SAYS

Did you see that 25% of the balls are blue? It is easiest to firstly find the answer as a decimal number, which is 0.25. Then convert this to a percentage by multiplying by 100, giving the answer of 25%.

ANSWERS

Question 9

In a packet of 200 stickers, 3⁄4 are gold. The rest are silver.

Which decimal number represents the number of silver stickers?

CORRECT ANSWER

0.25

EDDIE SAYS

Keep up the good work! Great job if you chose 0.25. Firstly, we had to work out that 1⁄4 of the stickers were silver as 3⁄4 were gold. Then we had to convert 1⁄4 to a decimal number by dividing the numerator by the denominator. 1 ÷ 4 = 0.25

ANSWERS

Question 10

In a packet of 300 stickers, 1⁄2 are gold. The rest are silver.

Which decimal number represents the number of silver stickers?

CORRECT ANSWER

0.5

EDDIE SAYS

Phew, that was a challenge! Nice job if you chose 0.5. Firstly, we had to work out that 1⁄2 of the stickers were silver as 1⁄2 were gold. Then we had to convert 1⁄2 to a decimal number by dividing the numerator by the denominator. 1 ÷ 2 = 0.5 Wow! That's another activity completed! How about attempting another one so you feel super confident?