Decimals with Repeater as a Fraction

by Campbell
(Sydney, Australia)

Turn a decimal into a fraction

rewrite 0.12 repeater as a fraction

Keep in mind that both a decimal and a fraction stand for part of a whole integer.

You can visualize this by thinking about cutting a wedge from an apple. The wedge (which can be represented by a decimal or a fraction) is a part of the apple, but not the whole apple.

Comments for Decimals with Repeater as a Fraction

 Jul 11, 2013 Decimal – Fraction – Equivalence by: Staff Answer Part I If 0.12 is not a repeating decimal, you can solve the problem like this: Since there are two numbers to the right of the decimal, the fraction is: 12/100 Or (the reduced form) 3/25 However, if 0.12 is does represent a repeating decimal, it should look like this: .(a)(a)(a)... “a” is called the “repetend” 0.1212121212 . . . Follow the next few steps to turn this repeating decimal into a fraction Multiply the repeating decimal by 100. You should use the number 100 because it will shift the decimal point exactly two digits. This is because the number which repeats itself is exactly two digits. (If the number which repeats itself was 3 digits, such as .123123123 . . ., then you would multiply by 1000 . . . and so on.) Let x stand for the repeating decimal x = 0.1212121212 . . . 100x = 100 * (0.1212121212 . . .) 100x = 12.1212121212 . . . ---------------------------------------------------------------------------

 Jul 11, 2013 Decimal – Fraction – Equivalence by: Staff ---------------------------------------------------------------------------Part IISubtract 1x from 100x 100x = 12.1212121212 . . .-x = - 0.1212121212 . . . -------    ----------------------99x = 12 Divide each side of the equation by 99 99x = 1299x / 99 = 12 / 99x = 12 / 99or, in its reduced formx = 4 / 33 ---------------------------------------------------------------------------

 Jul 11, 2013 Decimal – Fraction – Equivalence by: Staff --------------------------------------------------------------------------- Part III the final answer is: 0.1212121212 . . . = 4 / 33 Thanks for writing. Staff www.solving-math-problems.com