Write the fraction as a terminating or repeating decimal....

Key Concepts

Prime Factorization of the Denominator

Prime factorization of the denominator helps determine the nature of the decimal expansion. If the denominator factors completely into 2s and/or 5s, the decimal will be terminating. Conversely, if other primes are present, the decimal expansion will be repeating. This concept connects number theory with practical arithmetic conversions.

Long Division Method

The long division method is a step-by-step process used to divide the numerator by the denominator, which can reveal whether the resulting decimal terminates or repeats. This method is a practical tool for performing the conversion from fraction to decimal when a calculator is not used.

Repeating Decimal

A repeating decimal is a decimal in which a sequence of one or more digits repeats indefinitely. This happens when the denominator, in its simplest form, contains prime factors other than 2 or 5. Recognizing repeating decimals is important for distinguishing between different types of rational numbers.

Terminating Decimal

A terminating decimal is a decimal number that has a finite number of digits after the decimal point. This occurs when the fraction’s denominator (after simplification) has only the prime factors 2 and/or 5. Understanding which fractions convert to terminating decimals is crucial in number theory and arithmetic.

Fraction to Decimal Conversion

This concept involves converting a fraction into its decimal form by performing division of the numerator by the denominator. It is fundamental to understanding the relationship between fractions and decimals, and it is often accomplished through long division or by recognizing patterns in the division process.

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