Question

How do you know a fraction will have a terminating decimal?

Select all that apply.

Group of answer choices

When the denominator is a factor of 10, 100, 1,000, etc.

If the fraction can be simplified or rewritten with a denominator of 10, 100, or 1,000

If the fraction is greater than 1.

If the fraction is less than 1.

Answer 1

A fraction will have a terminating decimal " When the denominator is a factor of 10, 100, 1,000, etc." ⇒ A

A fraction will have a terminating decimal "If the fraction can be simplified or rewritten with a denominator of 10, 100, or 1,000" ⇒ B

Explanation:

Let us explain the meaning of terminating decimal

A terminating decimal is defined as a decimal number that contains a finite number of digits after the decimal point.

• All terminating decimals are rational numbers that can be written as fractions with denominators containing no prime number factors other than two or five, so we can change the denominators to 10, 100, 1000, 10000, ...........

Examples

• 3/5 ⇒ multiply up and down by 2, 3/5 = 6/10 (5 is a factor of 10)

• 39/25 ⇒ Multiply up and down by 25, 39/25 = 156/100 (25 is a factor of 100)

• 7/8 ⇒ Multiply up and down by 125, 7/8 = 875/1000 (8 is a factor of 1000)

• 13/400 ⇒ Multiply up and down by 25, 13/400 = 325/10000 (400 is a factor of 10000)

All these numbers are terminating decimals

That means the fraction is a terminating decimal if its denominator is a factor of 10, 100, 1000, ..........

A fraction will have a terminating decimal " When the denominator is a factor of 10, 100, 1,000, etc." ⇒ A

A fraction will have a terminating decimal "If the fraction can be simplified or rewritten with a denominator of 10, 100, or 1,000" ⇒ B