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Recurring decimals

How do you convert these decimals into fractions?
1). 0.8175 (with dots above the 7 and 5)
2) 0.47 (with a dot above the 7)
Original post by Lucofthewoods
How do you convert these decimals into fractions?
1). 0.8175 (with dots above the 7 and 5)
2) 0.47 (with a dot above the 7)


The trick is to arrange things so that you can make an equation that does not involve the infinite part of the number - you then solve the equation e.g.

Let a=2.03˙=2.03333⋯a = 2.0\dot{3} = 2.03333 \cdots.

Now multiply both sides by 10:

10a=20.3333⋯=20.33˙10 a = 20.3333 \cdots = 20.3\dot{3}

Can you now see how to get rid of the infinite list of 3s by using the two equations?

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