Math Is Fun Forum

mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Repeating or Terminating Decimal

A rational number is defined as the quotient of two integers. When written as a decimal, the decimal will either repeat or terminate. By looking at the denominator of the rational number, there is a way to tell in advance if it's decimal representation will repeat or terminate. What is "A WAY" to tell if it's decimal representation will repeat or terminate?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,637

Re: Repeating or Terminating Decimal

If the denominator has only powers of 2 and 5 the decimal form will terminate .

This because we use base 10 for our arithmetic.

Eg 1/40 = 1/(2x2x2x5)=(1x5x5)/(2×2×2×5×5×5)=25/1000=0.025

Bob

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Children are not defined by school ...........The Fonz
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mathxyz

Member

From: Brooklyn, NY

Registered: 2024-02-24

Posts: 1,053

Re: Repeating or Terminating Decimal

If the denominator has only powers of 2 and 5 the decimal form will terminate .

This because we use base 10 for our arithmetic.

Eg 1/40 = 1/(2x2x2x5)=(1x5x5)/(2×2×2×5×5×5)=25/1000=0.025

Bob

Is your work here called the prime factorization?