IXL - Write a repeating decimal as a fraction (Algebra 2 practice)

Write the repeating decimal as a fraction.

.44444444…

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question

Write the repeating decimal as a fraction.

.291291291…

key idea

A series is the sum of a sequence. The infinite series

is geometric if the ratios of consecutive terms are all defined and equal to the same number

(the common ratio of the series).

the sum of the series is:

–

solution

Identify the pattern in the repeating decimal.

.291291291…

Write this decimal as a sum by splitting it into pieces of the repeating pattern. Then, write each piece as a fraction.

.291291291…

0.291

0.000291

0.000000291

291

1,000

291

1,000,000

291

1,000,000,000

The repeating pattern has 3 digits, and 1,000 has 3 zeros. So, each piece of the sum is 291 times a power of

1,000

291

1,000

291

1,000,000

291

1,000,000,000

291

1,000

291

1,000

291

1,000

291

1,000

291

1,000

291

1,000

This is a geometric series. Use the formula for the sum of a geometric series to write it as a fraction. Plug in the first term,

291

1,000

and the common ratio,

1,000

–

291

1,000

291

1,000

291

1,000

291

1,000

–

1,000

291

999

So,

.291291291…

291

999

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Not feeling ready yet? These can help:

NN.10Find the value of an infinite geometric series

W.7Convert decimals between standard and expanded form using fractions

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