Friday 7 February 2020

0.9999999... approximated to fraction

How to convert recurring decimals into fractions.

E.g.

To find 0.9999999......

If x = 0.9999999999......
then 10 x = 9.999999999......
so 9 x will be equalled to 10x - x
which is 9.99999...... - 0.99999......
so to get the answer you just have to cancel out the .99999999......s
so 9 x = 9
9 divided by 9 <--------- as the amount of x
will get the fraction 9/9 which is 1


E.g.

To find 0.4444444444......

Take 0.444444444...... to be x
x = 0.4444444......
10 x = 4.4444444......
10 x - x = 9 x
4.44444444...... - 0.444444444...... = 4
9 x = 4
x = 4/9

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