How to change a decimal in to a fraction

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mathlete13 eNotes educator| Certified Educator

To convert a decimal into a fraction, we use an understanding of place value. In any decimal, the first position immediately to the right of the decimal point is called the tenths; to the right of that is the hundredths, then the thousandths, ten-thousandths, hundred-thousandths, and so on. Each place value indicates the value of the denominator of an equivalent fraction.

For example, 0.7 has a 7 in the tenths position, so when writing this number as a fraction, we would write 7/10 because it represents seven tenths. The decimal 0.51 written as a fraction is 51/100 because the decimal ends in the hundredths position and therefore, represents fifty-one hundredths.

For negative decimals, we make the fraction negative (e.g., -0.3 = -3/10). Mixed numbers, which contain both whole number parts and decimals, are written in a similar fashion, wherein the whole number is  placed in front of the fraction (e.g., 4.21 = `4 21/100` ). If necessary, any resulting fraction can be reduced.