Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form 0.abcd, where at least one of the digits a, b, c, or d is nonzero. Let be the number of distinct numerators obtained when numbers in S are written as fractions in lowest terms. For example, both 4 and 410 are counted among the distinct numerators for numbers in S because 0.3636 = + and 0.1230 10. Find the remainder when N is divided by 1000. 3333

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Let S be the set of all rational numbers that can be expressed as a repeating
decimal in the form 0.abcd, where at least one of the digits a, b, c, or d is
nonzero. Let be the number of distinct numerators obtained when numbers
in S are written as fractions in lowest terms. For example, both 4 and 410 are
counted among the distinct numerators for numbers in S because 0.3636 = +
and 0.1230
10. Find the remainder when N is divided by 1000.
3333
Transcribed Image Text:Let S be the set of all rational numbers that can be expressed as a repeating decimal in the form 0.abcd, where at least one of the digits a, b, c, or d is nonzero. Let be the number of distinct numerators obtained when numbers in S are written as fractions in lowest terms. For example, both 4 and 410 are counted among the distinct numerators for numbers in S because 0.3636 = + and 0.1230 10. Find the remainder when N is divided by 1000. 3333
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