Algebra Honors (Period 6 & 7)

Decimal Forms of Rational Numbers 11-2


Any common fraction can be written as a decimal by dividing the numerator by the denominator. If the remainder is zero, the decimal is called a terminating, or ending, or finite decimal.
3/8
Actually this is one of the fractions you need to know by heart !

If you don’t a remainder of zero when dividing the numerator by the denominator, continue to divide until the remainder begins to repeat.
5/6
7/11

3 2/7


The decimal quotient above are nonterminating, nonending, or infinite. The dots indicate that the decimals continue without end.

They are also called repeating or periodic because the same digit or block of digits repeats unendingly. A bar (vinculum) is used to indicate the block of digits that repeat.
What ones do you need to know by heat… same from 6th grade
1/3 family, 1/11 family, and let’s look at the 1/7 family (my favorite)

Let’s look at this algebraically… when you divide a positive integer n by a positive integer d, the remainder r at each step must be zero or a positive integer less than d. For example, if the divisor is 6, the reminders will be 0, 1, 2, 3, 4, or 5 and the division will terminate or begin repeating within 5 steps after only zeros remain to be brought down.
For every integer n and every positive integer d, the decimal form of the rational number n/d either terminates or eventually repeats in a block of fewer than d digits.