Question

Write the fraction as a terminating or repeating decimal. $$ \frac{3}{4} $$

   Write the fraction as a terminating or repeating decimal.
$$
\frac{3}{4}
$$

Algebra 1: Concepts and Skills

Algebra 1: Concepts and Skills

Ron Larson, Laurie… 1st Edition

Chapter 9, Problem 102

Instant Answer

Solved by Expert Ramzi Deek

04/18/2020

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In this case, we divide 3 by 4. Show more…

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Write the fraction as a terminating or repeating decimal. $$ \frac{3}{4} $$

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Key Concepts

Rational Numbers

Rational numbers are numbers that can be expressed as the quotient of two integers, where the denominator is not zero. This definition ensures that every rational number can be represented either as a terminating or a repeating decimal when converted appropriately, laying the foundation for understanding their decimal expansions.

Decimal Representation

Decimal representation of numbers involves expressing a number in base-10 format. Rational numbers, when written as decimals, may either have a finite number of digits (terminating) or a sequence of digits that repeat indefinitely (repeating), depending on the factors in the denominator after the fraction is simplified.

Terminating Decimals

A terminating decimal is one that has a finite number of digits after the decimal point. This occurs when the denominator of the simplified fraction has no prime factors other than 2 and 5, which are the prime factors of the base number 10.

Repeating Decimals

A repeating decimal is one where one or more digits repeat infinitely. This occurs when the simplified fraction’s denominator contains prime factors other than 2 and 5. Recognizing repeating decimals is crucial in understanding how rational numbers can be represented in a non-terminating, but still patterned form.

Conversion of Fractions to Decimals

Converting fractions to decimals typically involves division - dividing the numerator by the denominator. This process helps determine whether the decimal representation terminates or repeats, and can be done using long division or by analyzing the prime factors of the denominator.

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