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One-third and one-quarter fractions.
Do you know how to write fractions like ¼ as decimals?

Decimal Numbers 2 (Medium)

Dive deeper into decimals with this 11 Plus Maths quiz. Learn how repeating and non-repeating decimals behave in fascinating mathematical patterns.

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Fascinating Fact:

The number pi starts at 3.14159265 and goes on forever without repeating, proving that even decimals can be infinite.

In 11 Plus Maths, decimals are explored through their patterns and precision. Students learn to understand recurring and terminating decimals, rounding methods, and their everyday uses.

  • Pi (?): A mathematical constant that represents the ratio of a circle’s circumference to its diameter.
  • Recurring Decimal: A decimal that repeats a sequence of digits forever, such as 0.3333.
  • Terminating Decimal: A decimal that ends after a certain number of digits, like 0.25.
What does a repeating decimal mean?

A repeating decimal shows a pattern that goes on forever, such as 0.121212. These are also called recurring decimals.

How is pi (?) used in maths?

Pi is used to calculate the circumference and area of circles. Its decimal never ends or repeats, making it an example of an infinite number.

What’s the difference between recurring and terminating decimals?

Recurring decimals repeat forever, while terminating decimals stop after a few digits. For example, 1/3 = 0.333... and 1/4 = 0.25.

1 .
If you divide 221 by 1,000, what number do you get?
0.0221
22.1
2.21
0.221
If you divide by 1,000, move the digits 3 places to the right. The decimal point in whole numbers cannot be seen, but it can be imagined as coming straight after the number, followed by zeros (i.e. 221 = 221.000)
2 .
What is 0.125 as a fraction?
16
17
18
19
100 ÷ 8 = 12.5. and 12.5 ÷ 100 = 0.125
3 .
If you multiply 0.024 by 1,000, what number do you get?
240
0.24
2.4
24
If you multiply by 1,000, move the digits 3 places to the left
4 .
What is 0.333 as a fraction?
27
14
13
25
1?3 as a decimal is 0.33333 - the 3s go on forever. We call this 'recurring'.
5 .
What is ‘one-fifth’ as a decimal?
0.12
0.2
0.25
0.125
100 ÷ 5 = 20 so 1 ÷ 5 = 0.2
6 .
What is 0.75 as a fraction?
34
23
45
35
75 is 3 x 25, and we know that 25 is one-quarter of 100. So, 0.75 is three-quarters of 1.
7 .
What is ‘three-eighths’ as a decimal?
0.375
0.333
0.425
0.412
To work this out, first divide 100 by 8 to get 12.5. Next multiply 12.5 by 3 to get 37.5. Finally, divide 37.5 by 100 to get the answer 0.375
8 .
What is ‘one-hundredth’ as a decimal?
0.1
0.01
0.001
0.0001
The columns after the decimal point are tenths, hundredths, thousandths, ten-thousandths etc.
9 .
What is 0.666 as a fraction?
45
34
23
56
2?3 as a decimal is 0.666 recurring (that means the 6s go on forever!).
10 .
If you turn ‘one-fifth’ into a decimal and then multiply by 10, what is the answer?
25
2
200
20
1 ÷ 5 = 0.2 and 0.2 x 10 = 2
Author:  Frank Evans (Specialist 11 Plus Teacher and Tutor)

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