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How do you convert 0.03 (3 repeating) to a fraction?

Answer 1

#0.0bar(3) = 1/30#

As a general method for converting repeating decimals to fractions, suppose that the repeating portion is #n# digits long. Then let #x# represent the initial value, and using the fact that #10^nx-x# has finitely many digits, solve for #x# to find the fraction.

In this case, #3# is the repeating portion, which has #1# digit. Thus, we will let #x=0.0bar(3)# (the bar denotes repeating digits) and multiply by #10^1#.

#x = 0.0bar(3)#

#=>10x = 0.bar(3)#

#=>10x-x = 0.bar(3)-0.0bar(3)#

#=> 9x = 0.3#

#=> x = 0.3/9 = 3/90 = 1/30#

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Answer 2

Hazel Anglin

To convert 0.03 (repeating) to a fraction, first, let x = 0.03 (repeating). Then, multiply both sides by 100 to eliminate the repeating decimal:

100x = 3.03 (repeating)

Subtract the original equation from the multiplied one:

100x - x = 3.03 (repeating) - 0.03 (repeating) 99x = 3

Now, divide both sides by 99:

x = 3/99

Reduce the fraction:

x = 1/33

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Answer 3

Eva Adamson

0.03 (repeating) as a fraction is 1/33.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.