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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 92E
icon
Related questions
Question
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
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Elements Of Modern Algebra
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning