Understanding Decimal Expansions and Prime Factorization

What is the main difference between terminating and repeating decimals?

• Repeating decimals are always less than 1.

• Terminating decimals are always greater than 1.

• Repeating decimals have a finite number of digits.

• Terminating decimals have a finite number of digits.

Which of the following fractions has a repeating decimal expansion?

• 1/5

• 1/4

• 1/3

• 1/2

What is the decimal expansion of 1/3?

• 0.33

• 0.3333

• 0.333...

• 0.3

What is the prime factorization of the number 10?

• 5 * 7

• 2 * 3

• 3 * 5

• 2 * 5

Which of the following fractions has a terminating decimal expansion?

• 1/6

• 1/8

• 1/9

• 1/7

Why do fractions with denominators consisting only of 2s and 5s have terminating decimals?

• Because they are divisible by 10.

• Because they are even numbers.

• Because they are odd numbers.

• Because they are prime numbers.

What is the significance of the prime factors 2 and 5 in decimal expansions?

• They determine if a decimal is terminating.

• They determine if a decimal is repeating.

• They determine if a decimal is less than 1.

• They determine if a decimal is greater than 1.

What happens to the decimal expansion of a fraction if its denominator has factors other than 2 and 5?

• It becomes a terminating decimal.

• It becomes a repeating decimal.

• It becomes an irrational number.

• It becomes a whole number.

Which of the following is an example of an irrational number?

• 0.5

• 3/4

• 1/2

• Pi

Why can't irrational numbers be expressed as fractions?

• Because they have non-repeating, non-terminating decimals.

• Because they are whole numbers.

• Because they have terminating decimals.

• Because they have repeating decimals.