Transcript BITS AND PIECES III INVESTIGATION 3.4 REPRESENTING

BITS AND PIECES III
INVESTIGATION 3.4
REPRESENTING FRACTIONS AS DECIMALS
What are terminating decimals?
Terminating decimals are numbers that do not
repeat when divided.
When you take 1 and divide it by 2, you
get 0.5. When you take 1 and divide it
by 4, you get 0.25.
What are repeating decimals?
What are repeating decimals?
Repeating decimals are numbers that
repeat. When doing 1 divided by 3 the
number never ends and continuously
repeats 3 after 0. When doing 1 divided
by 11 the number never ends and
continuously repeats 09 after 0.
Why do fractions like 1/2 and 1/4 also
have terminating decimal forms?
Why do fractions like 1/2 and 1/4 also
have terminating decimal forms?
Because they can make equivalent
fractions with denominators of 10, 100,
1000, etc. 1/2 = 5/10; 1/4 = 25/100
1.) 2/5 = 4/10 = 0.4
2.) 3/8 = 375/1000 = 0.375
3.) 5/6 is Repeating = 0.83333......
4.) 35/10 = 3.5
5.)8/99 is Repeating = 0.8888......
1.) 2/5 = 4/10 = 0.4
2.) 3/8 = 375/1000 = 0.375
3.) 5/6 is Repeating = 0.83333......
4.) 35/10 = 3.5
5.)8/99 is Repeating = 0.8888......
1/4, 2/8, 4/16, 5/20, 6/24, 25/100 = 0.25
The decimal matches the fraction that has 10,
100, 1000, etc. as a denominator 25/100 = 0.25
35/100
21456/10000
89050/100000= 8905/10000
214560/100000= 21456/10000
1/3, 1/6, 1/9, 5/15
1. To tell whether a fraction has a terminating or repeating
decimal representation, examine it in its simplest form.
Fractions with terminating decimals only have 2’s and/or 5’s
in the prime factorization of the denominator. Fractions with
repeating decimals will have factors other than 2 or 5 in the
denominator.
2. There is no repeating decimal with 10, 100, 1000, etc. as
its denominator.