# Conversion of fractions to Decimal representation

State whether each of the following fraction is a terminating or repeating decimal. If the decimal terminates, state the number of decimal places and show how you decided. IF the decimal repeats, write the decimal representation of the fraction.

a. 12/32

b. 6/2^2 x 5^7 x 3

^meaning exponent!

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#### Solution Preview

<br>In addition to the solution here you might want to visit

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<br>http://mathworld.wolfram.com/RepeatingDecimal.html

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<br>Solution:

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<br>a. 12/32=3/8

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<br>=3/(2^3)=3*(5/10)*(5/10)*(5/10)=(3*5*5*5)/10^3

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<br>Therefore we have three decimal digits (The numerator is odd and therefore can not be a multiplication of 10)

<br>and they are terminating decimals (0.375)

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<br>For part B it is hard to understand the format of the fraction.

<br>If one stick to the conventions it should read:

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<br>[6/(2^2)] * (5^7) * (3)

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<br>The ...