How to Write Repeating Decimals as Fractions

The video tutorial explains that repeating decimals are rational numbers and can be expressed as fractions. It demonstrates the algebraic process of converting repeating decimals into fractions using examples like 0.3 repeating, 0.7 repeating, and 0.352 repeating. The tutorial also provides practice problems for viewers to try on their own.

What is the definition of a rational number?

• A number that cannot be expressed as a fraction

• A number that can be written as the ratio of two integers

• A number that is always an integer

• A number that is always irrational

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

• Multiply the decimal by 10

• Let X equal the repeating decimal

• Divide by the number of repeating digits

• Subtract the repeating part

How do you determine the number to multiply by when converting a repeating decimal with one repeating digit?

• Multiply by 1

• Multiply by 100

• Multiply by 10

• Multiply by 1000

What is the fraction equivalent of 0.7 repeating?

• 2/3

• 1/3

• 7/9

• 5/9

When converting a decimal with two repeating digits, what do you multiply by?

• 10

• 100

• 1000

• 1

What is the fraction form of 0.352 repeating?

• 352/999

• 35/99

• 352/1000

• 35/100

How do you handle a negative repeating decimal when converting to a fraction?

• Multiply by a negative number

• Convert as a positive number

• Add the negative sign after conversion

• Ignore the negative sign