Pre-Algebra 14.15

To keep things moving, let us try the fraction 1/8. We begin with the first digit at the 1/10 position. Right away, the fraction 1/10 is the closest-under (with denominator 10) to 1/8. 1 is then the first decimal digit. We can then subtract 1/10 from 1/8 to determine the remainder, which is 1/40. The second digit is the 1/100 position, to be filled by the closest-under denominator-100 fraction to 1/40. The lowest-term equivalents to 1/40 are 2/80 and 3/120. 3/100 is larger than 3/120, but 2/100 is smaller than 2/80. So the second digit is 2. This still leaves a difference when we subtract 2/80 – 2/100. That difference is 5/1000, giving us 5 for the third digit, the 1/1000 position. The sum of 1/10, 2/100, and 5/1000 exactly equals the fraction 1/8 as you can verify with your fraction-addition skills (or calculator).

Decimals

Numbers and Arithmetic

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