Converting Repeating Decimals to Fractions

The video tutorial by Professor Von Schmohawk explains how to convert repeating decimal numbers into fractions. It covers the process of eliminating repeating digits by multiplying and subtracting the original number, forming equations, and simplifying them to find the equivalent fraction. Examples include decimals with single repeating digits, multiple repeating digits, and complex sequences. The tutorial concludes with a brief introduction to the next topic, exponentiation.

What happens to the digits of a decimal number when it is multiplied by ten?

• They shift one column to the right.

• They shift one column to the left.

• They remain unchanged.

• They double in value.

How do you eliminate the repeating digit in a repeating decimal number?

• By dividing the number by ten.

• By subtracting ten from the number.

• By multiplying the number by ten and then subtracting the original number.

• By adding the number to itself.

What is the fraction equivalent of the repeating decimal 0.555...?

• 5/10

• 1/2

• 5/9

• 1/3

What is the simplified fraction form of the repeating decimal 0.333...?

• 1/3

• 1/4

• 1/5

• 1/2

How do you handle a repeating sequence of three digits in a decimal number?

• Multiply by 1000 and subtract the original number.

• Multiply by 10000 and subtract the original number.

• Multiply by 10 and subtract the original number.

• Multiply by 100 and subtract the original number.

What is the fraction equivalent of the repeating decimal 0.123123...?

• 123/999

• 123/1000

• 123/100

• 123/90

What is the first step in converting the repeating decimal 0.1666... to a fraction?

• Divide by 10.

• Multiply by 10.

• Multiply by 100.

• Subtract 1.

What fraction does the repeating decimal 0.1666... simplify to?

• 1/8

• 1/5

• 1/6

• 1/7

How many columns do you shift a number with six repeating digits to the left?

• Three columns

• One column

• Ten columns

• Six columns

What is the fraction equivalent of the repeating decimal 0.142857142857...?

• 1/6

• 1/7

• 1/8

• 1/9