Select the decimal that is equivalent to 111/250

The answer is 0.444.

Note the following pattern for repeating decimals:

0.22222222... = 2/9

0.54545454... = 54/99

0.298298298... = 298/999

Division by 9's causes the repeating pattern.

Note the pattern if zeros precede the repeating decimal:

0.022222222... = 2/90

0.00054545454... = 54/99000

0.00298298298... = 298/99900

Adding zero's to the denominator adds zero's before the repeating decimal.

To convert a decimal that begins with a non-repeating part, such as 0.21456456456456456..., to a fraction, write it as the sum of the non-repeating part and the repeating part.

 0.21 + 0.00456456456456456...

Next, convert each of these decimals to fractions. The first decimal has a divisor of power ten. The second decimal (which repeats) is converted according to the pattern given above.

 21/100 + 456/99900

Now add these fraction by expressing both with a common divisor

 20979/99900 + 456/99900

and add.

 21435/99900

Finally simplify it to lowest terms

 1429/6660

and check on your calculator or with long division.

= 0.2145645645...

111/250 in decimal is 0.444

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