The rational numbers that can be expressed as a repeating decimal are the ones that cannot be simplified to a fraction with a denominator that only contains 2's and 5's as prime factors.
78 = 39 * 2 = 3 * 13 * 2
512 = 256 * 2 = 2^9
1725 = 3^2 * 5^2 * 23
3140 = 2^2 * 5 * 157
Out of these numbers, only 78 can be expressed as a repeating decimal because it is the only one that does not have a denominator with only 2's and 5's as prime factors.
Which of the following rational numbers can be expressed as a repeating decimal: 78, 512, 1725, or 3140?(1 point)
2 answers
Which of the following rational numbers can be expressed as a repeating decimal: 7/8
, 5/12
, 17/25
, or 31/40
?
, 5/12
, 17/25
, or 31/40
?
1 answer