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Fraction Conversion

This document discusses two methods for converting between fractions and decimals. Method 1 uses factors of 10, 100 or 1000 to convert fractions to decimals by moving the decimal point. Method 2 uses long division. To convert decimals to fractions, the place value is identified and the decimal is written as an equivalent fraction with the appropriate denominator of 10, 100 or 1000. Examples are provided to demonstrate both conversion methods.

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297 views3 pages

Fraction Conversion

This document discusses two methods for converting between fractions and decimals. Method 1 uses factors of 10, 100 or 1000 to convert fractions to decimals by moving the decimal point. Method 2 uses long division. To convert decimals to fractions, the place value is identified and the decimal is written as an equivalent fraction with the appropriate denominator of 10, 100 or 1000. Examples are provided to demonstrate both conversion methods.

Uploaded by

LondonMathsTutor
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Conversion 1 - Decimals and fractions

____________________________________________________________________
Convert Fractions to Decimals

There are two possible ways to do the conversion. The first method can be used as
long as you are able to spot the factors of 10, 100, 1000 in the denominators. The
second method applies to all fractions.

Method 1 – Using factors of 10, 100, 1000

7 7 4

25 25  4
1. Find the equivalent fraction with the
denominator of 10,100,1000, etc
28
 (i.e. 28  100 ) 2. Move the decimal point to the left, the number
100
of times depending on the number of zero.
= 0.28

Factors of 10,100 and 1000

10 100 1000
1 x 10 1 x 100 1 x 1000
2x5 2 x 50 2 x 500
4 x 25 4 x 250
5 x 20 5 x 200
10 x 10 8 x 125
10 x 100

More working examples using method 1.

5 7125 4 4 2 7 7 5
  
8 8 125 5 5 2 20 20  5

625 8 35
  
1000 10 100

 0.625  0.8  0.35

ukmathstutor@gmail.com London Maths Tutor


Conversion 1 - Decimals and fractions
____________________________________________________________________

Method 2 – Long Division

7 0.28

25

Long division steps:

1. 25 can’t go into 7, add a zero and a


2 decimal point after 7
2. Bring the decimal point up and add a
zero in front of the decimal point.

3. Divide 70 by 25, 2 remaining 20.

4. Add another zero and bring it down to


3 make the remainder to 200.

5. Divide 200 by 25, which is 8.

6. Answer is 0.28

ukmathstutor@gmail.com London Maths Tutor


Conversion 1 - Decimals and fractions
____________________________________________________________________
Convert decimals to fractions

You first need to recognise the place value of the decimal before converting to
appropriate fractions:

1) Decimal reading:

0.1  This reads as 1 tenth (one decimal place)

0.14  This reads as 14 hundredths (two decimal places)

0.234  This reads as 234 thousandths (three decimal places)

2) Converting to fractions:

x x x
Tenth  Hundredths  Thousandths 
10 100 1000

Working Example:

4
0.4 
10 1. Read the decimal mentally
4 2 (I.e. read as 4 tenths)

10  2
2 2. Write the fraction based on the reading

5
3. Reduce the fraction to its lowest term.

Revision Exercise

Change the following fractions to decimal.

1 2 66 382 27
1) 2) 3) 4) 5)
4 8 19 100 25

11 3 6 14 923
6) 7) 8) 6 9) 1 10 3
50 10 9 25 1000

Convert decimal to fraction

1) 0.83 2) 0.19 3) 0.35 4) 1.325 5) 3.03

6) 2.25 7) 5.52 8) 4.90 9) 8.5 10 9.11

ukmathstutor@gmail.com London Maths Tutor

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