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Physicss Physics A Level Physics Home Revision hut
Fractions, Decimals
and Percentage
These can all be used to represent
a part of a whole amount.
the animation below shows how to convert
between them
Decimal to fraction
If there is one number to the right of the decimal point
write down the number ( ignoring the decimal point)
and put it over 10,then simplify the fraction to it’s
lowest  form
eg.  0.4  =  4    = 2

If there are 2 numbers to th right of the decimal point
write down the number (as above) but this time put it over
100 and simplify to it’s lowest form
If there are 3 numbers put over 1000 and do the same
Fraction to decimal
Divide the top number by the bottom number
eg.    3  =  0.6


Fraction to percent
Divide the top number by the bottom number then multply
the answer by 100
eg.  3    =  0.75 x 100 = 75%


Percent to fraction
Put over 100 and simplify
eg  60% = 60  =  6  = 3



Decimal to percent
multiply by 100 (or move the decimal point 2 places to
the right)

eg,  0.3  x 100 = 30%

     0.45  x 100  = 45%     0.235 x100  = 23.5%

Percent to Decimal
Do the opposite of above, divide by 100 (move the decimal
point 2 places to the left)

eg.  30%  = 30/100 =0.30 (0.3)

      45% = 45/100 =0.45

To simplify a fraction
Make a list of the factors of the numerator (top number) and the
denominator (bottom number) then find the highest number which
appears in both lists.
Divide both top and bottom numbers by this number.
example

    8     factors of 8 are  2 and 4
   12    factors of 12 are 2, 3, 4, and 6
          4 is the highest number in both lists
divide this into both 8 and 12 and you get 2
                                                                        3
so the simplest form of  8  is 2
                                        12     3
try 18    factors 2, 3, 6, and 9
      30    factors  2, 3, 5, 6, 10 and 15
6 is the highest number in both lists
divide this into both 18 and 30 and you get  3
                                                                           5
( if this method looks familiar it’s the same as finding the
highest common factor of two numbers described in the factors section)


           
10 5


4
100 10 5 Equivalent fractions
1
2
2
4
4
8
3
6
All the blue parts are equivalent fractions
1
2
is the simplest form
You can find an equivalent fractions by
multiplying the top (numerator) and the bottom
(denominator) by the same number.
Example
3
4
x 6 x 6 = 18
24
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