Understanding Fractions and Decimals

The video tutorial explains the classification of rational numbers into terminating and non-terminating recurring decimals. It demonstrates how to determine the type of decimal by analyzing the prime factors of the denominator. The tutorial provides examples of rational numbers and explains the process of prime factorization to identify whether a decimal is terminating or non-terminating recurring. The key takeaway is that if the prime factors of the denominator are only 2 or 5, the decimal is terminating; otherwise, it is non-terminating recurring.

What are the two types of decimals that rational numbers can be classified into?

• Even and odd

• Positive and negative

• Whole and fractional

• Terminating and non-terminating recurring

Which of the following is a characteristic of a terminating decimal?

• Digits after the decimal point repeat indefinitely

• Decimal value is less than 0

• Digits after the decimal point end

• Decimal value is greater than 1

What is the decimal form of the fraction '5 by 2'?

• 0.25

• 5.2

• 0.5

• 2.5

Which fraction results in a non-terminating recurring decimal?

• 5 by 2

• 9 by 20

• 8 by 15

• 17 by 5

What is the prime factorization of the denominator in the fraction '8 by 15'?

• 2 x 3

• 2 x 5

• 3 x 5

• 5 x 7

How can you determine if a decimal is terminating by looking at the denominator?

• If the denominator is an even number

• If the prime factors of the denominator are only 2 and/or 5

• If the denominator is a multiple of 7

• If the denominator is a multiple of 3

What is the prime factorization of 20?

• 2^2 x 5

• 5 x 4

• 2 x 10

• 3 x 7

Which of the following fractions has a denominator with a prime factor other than 2 or 5?

• 5 by 2

• 9 by 20

• 17 by 5

• 11 by 21

What is the general form of the denominator for a terminating decimal?

• 5^m x 7^n

• 2^m x 5^n

• 2^m x 3^n

• 3^m x 7^n

What additional factor is present in the denominator of a non-terminating recurring decimal?

• A factor of 2

• A factor of 5

• A factor of 10

• A prime factor other than 2 or 5