Convert Decimals to Fractions Quiz and Flashcards

Study Notes

Converting Decimals into Fractions

Mixed Numbers

A mixed number is a combination of a whole number and a proper fraction
Example: 2 3/4 (2 is the whole number, 3/4 is the fraction)
To convert a decimal to a mixed number, separate the whole number part from the fractional part
Example: 2.75 = 2 3/4 (whole number part is 2, fractional part is 0.75 = 3/4)

Equivalent Ratios

Equivalent ratios are fractions that have the same value but different numerators and denominators
Example: 1/2 = 2/4 = 3/6 (these fractions have the same value but different numerators and denominators)
To find an equivalent ratio, multiply or divide both numerator and denominator by the same number
Example: 1/2 = (1 x 2)/(2 x 2) = 2/4 (multiplied numerator and denominator by 2)

Simplifying Fractions

Simplifying a fraction means reducing it to its simplest form
To simplify a fraction, divide both numerator and denominator by their greatest common divisor (GCD)
Example: 6/8 = (6 ÷ 2)/(8 ÷ 2) = 3/4 (simplified fraction)

Improper Fractions

An improper fraction is a fraction where the numerator is greater than or equal to the denominator
Example: 3/2, 5/3
To convert an improper fraction to a mixed number, divide the numerator by the denominator
Example: 3/2 = 1 1/2 (divided numerator by denominator and separated whole number part from fractional part)

Repeating Decimals

A repeating decimal is a decimal that has a sequence of digits that repeats indefinitely
Example: 0.12341234... (the sequence "1234" repeats indefinitely)
To convert a repeating decimal to a fraction, use the following formula:
- Let x = the repeating decimal (e.g. x = 0.12341234...)
- Multiply x by 10^n, where n is the number of digits in the repeating sequence (e.g. 10^4, since the sequence "1234" has 4 digits)
- Subtract x from the result to get a fraction
- Simplify the fraction
Example: 0.12341234... = x
- 10^4x = 1234.12341234...
- 10^4x - x = 1234
- 9999x = 1234
- x = 1234/9999 (simplified fraction)

Description

Learn how to convert decimals to fractions, including mixed numbers, equivalent ratios, simplifying fractions, and improper fractions. Practice converting repeating decimals to fractions using a simple formula.