a decimal expansion; for rational numbers show that the decimal ... equations by moving the decimal point in both locations. Examples. Convert to a fr...
18.5 More Complex 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 Convert to a fraction. 1) .4
2) .81
Evaluate the expressions. 3) 10 ÷ .2
10 4) .2
5) 6 ÷ .03
6)
6 .03
More Complex Repeating Decimals to Fractions Do all repeating decimals end up over 9, 99, and 999?
x = .16
10x = 1.66 − x = .16 9x = 1.5 9
9 15 ÷15 1 x= = 90 ÷15 6
NOTES Remember that we always need to simplify our fractions. Examples Convert to a fraction.
.12
.34
NOTES For mixed numbers its easiest to leave out the whole number until the end. Examples Convert to a fraction.
7.2
4.81
NOTES The number of repeating digits determines whether we multiply by 10, 100, or 1000 not their location -- but repeating digits still need to line up. Concept Check Set-up the equation to convert to a fraction.
.03
.02
NOTES We can clear decimals from fractions the same as equations by moving the decimal point in both locations. Examples Convert to a fraction.
.03
10x = .33
.02
10x = .22
− x = .03
− x = .02
9x = .3
9x = .2
EXAMPLES Convert to a fraction.
.07
Convert to a fraction. (hint there is a one in the numerator)
.083
PRACTICE Convert the decimal to a fraction.
1.8
.56
PRACTICE Convert the decimal to a fraction.
.06
FINAL QUESTION Convert to a fraction (hint there is a one in the numerator).
