Converting Fractions to Repeating Decimals

The video tutorial explains how to convert fractions into decimals, particularly when the denominator cannot be easily converted into a power of 10. It demonstrates the use of long division to find repeating decimals and introduces the notation for repeating sequences. The tutorial provides examples, such as converting 7/22, and shows how to simplify conversions using known results.

What is the first step in converting a fraction to a decimal?

• Divide the numerator by the denominator

• Multiply the fraction by 10

• Turn the denominator into a power of 10

• Turn the numerator into a power of 10

Why can't we turn 1/3 into a fraction with a power of 10 in its denominator?

• Because 3 is too large

• Because 3 is not in the prime factorization of powers of 10

• Because 3 is too small

• Because 3 is not a prime number

What does the bar over the 3 in 0.3̅ represent?

• It means the decimal terminates

• It means the decimal is rounded

• It means the decimal repeats forever

• It means the decimal is approximate

What is the repeating decimal representation of 1/3?

• 0.3̅

• 0.333

• 0.33

• 0.3

Why can't we convert 7/22 directly into a fraction with a power of 10 in its denominator?

• Because 22 is not a prime number

• Because 22 has a factor of 11

• Because 22 is an even number

• Because 22 is too large

What is the repeating decimal representation of 7/22?

• 0.318̅

• 0.3181

• 0.318

• 0.3181̅8̅

In the decimal 0.318̅, which digits are repeating?

• 8

• 3 and 1

• 1 and 8

• 3

How can we simplify the conversion of a fraction with a large denominator?

• By using long division

• By multiplying by 10

• By using previous results

• By adding zeros to the numerator

What is the decimal representation of 7/220?

• 0.0318

• 0.00318

• 0.0318̅

• 0.318

What happens when you multiply a decimal by 0.1?

• The decimal becomes smaller

• The decimal becomes larger

• The decimal point moves one place to the left

• The decimal point moves one place to the right