Question

Represent 1$/ 7$ and 4$/ 27$ as repeating decimals.

   Represent 1$/ 7$ and 4$/ 27$ as repeating decimals.

Calculus for AP

Calculus for AP

Jon Rogawski & Ray… 2nd Edition

Chapter 1, Problem 34

Instant Answer

Solved by Expert Aymara Gallardo

08/06/2019

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We can do this by dividing the numerator by the denominator. Show more…

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Represent 1$/ 7$ and 4$/ 27$ as repeating decimals.

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Key Concepts

Rational Numbers

Rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Their decimal representations either terminate after a finite number of digits or repeat cyclically. This property is a fundamental characteristic that can be used to classify and understand the nature of numbers in mathematical analysis.

Fraction to Decimal Conversion

Fraction to decimal conversion is the process of expressing a fractional number as a decimal, using methods such as long division. This conversion reveals whether the result is a terminating decimal or one that has a repeating pattern. Understanding this process is critical for working with both rational and irrational numbers.

Repeating Decimals

Repeating decimals are decimals that, after a certain point, have a sequence of digits that repeats indefinitely. This occurs when the denominator of the fraction (when in simplest form) contains prime factors other than 2 or 5. Recognizing and identifying repeating patterns is essential for accurately representing fractional values in decimal form.

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