decimal expansion which repeats eventually into a rational number. ... the original equation from the first and clear the repeating digits. Examples. ...
18.4 Repeating Decimals to Fractions 8. NS.1 Know that there are numbers that are not rational, and approximate them by rational numbers. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
WARM-UP Solve the equation (hint answers are fractions). 1) 10x = x + 7
2) 100x = x + 13
Evaluate the expressions. 3) .8 × 10
4) .88 × 100
5) .888 × 1000
Repeating Decimals to Fractions If fractions can be converted to repeating decimals, can they be converted back?
1 = .3 3
1 .3 = 3
NOTES To convert a repeating decimal to a fraction we need to create an equation and multiply both sides by 10, 100, or 1000 depending on the number of repeating digits. Concept Check Multiply both sides of the equation by 10.
x = .2
x = .3
Multiply both sides of the equation by 100.
x = .45
x = .09
NOTES We can then use the Property of Equality to subtract the original equation from the first and clear the repeating digits. Examples Convert to a fraction.