Let S be the set of all rational numbers that can be expressed as a repeatingdecimal in the form 0.abcd, where at least one of the digits a, b, c, or d isnonzero. Let be the number of distinct numerators obtained when numbersin S are written as fractions in lowest terms. For example, both 4 and 410 arecounted among the distinct numerators for numbers in S because 0.3636 = +and 0.123010. Find the remainder when N is divided by 1000.3333

Answered: Image /qna-images/answer/e9265d29-b759-481e-9615-7fee399d7412.jpg

Answered: Let S be the set of all rational…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

3. Show that 3.141592592592592... is a rational number, by expressing it as a ratio of two integers.
Suppose you divide a natural number n by a positive rational number less than 1. Will theanswer always be less than n, sometimes less than n, or never less than n? Why?
10 ation: an integer or rational number in the
4. State whether the given values are rational or irrational: 3. Brod convertedto a decimal, and his result was a repeating decimal. Does this mean that the value is rational or irational? Explain your answer. 0. 3.4567 b. 3.4567... C. 3.4567
Suppose that a positive number a is written in scien- tific notation as a = c × 10", where n is an integer and 1 sc< 10. Explain what n indicates about the size of a.
From the list 0, √2, 3/4, -5/6, 25/3 , -√3, -8, 0.34, 0.2 ̅3, 67, and 9/7 , identify each of the following.(a) The natural numbers(b) The integers(c) The nonnegative integers(d) The rational numbers(e) The irrational numbers
Determine the following number is rational or not, if it is irrational,prove your result, if it is rational, simply to fractional expression:x = √3/2
Consider the list of numbers: 2n-1, where n first equals 2, then 3, 4, 5,6,…What is the smallest value of n for which 2n -1 is not a prime number. Show all your work.
5. Look at some decimal expressions of fractions such as 325' 5' 15' 20' 14' 50 1 7 9 16 71 50 91 by carrying out long divisions or using your calculator (Careful, calculators can give mis- leading results!), and see which numbers have a terminating decimal expression, while paying attention to the prime factorisation of the denominator. Hint: Take a terminating decimal expression and see what happens when you convert it to a fraction in lowest terms. (Don't include this part in your homework submission.) Now come up with a conjecture for which fractions have a terminating decimal expres- sion. Your conjecture should be of the following form: Let a, b EN with b > 1 and with gcd(a, b) = 1. Then a has a terminating decimal expression iff .... Now prove your conjecture. Note that this is an “if and only if” statement, requiring proofs for both implications.
show that there does ot exist a rational numbers such that s2 = 6
1. List 4 numbers between -1 and 1 2. List 3 integers between -10 and 10 3. List all the rational numbers between 5 and 10. Is this an casy task to complete? Give reasons for your answer. 4. List all the real numbers between O and 20. Is this an easy task to complete? Give reasons for your answer. 5. How many integers are there between O and 20? 6. How many rational numbers are there between O and 20? 7. How many whole numbers are there between O and 20? B. Explain how the density property applies to a number system. 9. List two number systems that have the density property and two that do not. 10. State the limit of each sequence 20.3, 0.33, 0.333, 0.3333, . b. 12, 23, 34, 45, 56, 67, . c. 9.4, 9.04, 9.004, 9.0004, 9.00004, . d. 51, 54, 59, 516, 525, 549, -

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS