Math

QuestionConvert the repeating decimal 0.450.\overline{45} to a fraction.

Studdy Solution

STEP 1

Assumptions1. We are given a repeating decimal 0.450.\overline{45}. . We need to convert this repeating decimal into a fraction.

STEP 2

Let's denote the repeating decimal as xx.
x=0.45x =0.\overline{45}

STEP 3

Since 4545 is the repeating part, we multiply both sides of the equation by 100100 (because 4545 is a two-digit number) to shift the decimal point two places to the right.
100x=45.45100x =45.\overline{45}

STEP 4

Now, subtract the original equation from this new equation to eliminate the repeating part.
100xx=45.450.45100x - x =45.\overline{45} -0.\overline{45}

STEP 5

implify the left side of the equation and the right side of the equation.
99x=4599x =45

STEP 6

Finally, solve for xx by dividing both sides of the equation by 9999.
x=4599x = \frac{45}{99}

STEP 7

implify the fraction to its lowest terms.
x=511x = \frac{5}{11}So, the repeating decimal 0.450.\overline{45} can be written as the fraction 511\frac{5}{11}.

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