Introduction:
Every fraction (i.e. rational number) can be written in decimal form. So how do
you rename fractions (the terminating kind) as decimals?
Find an equivalent fraction that has 10, 100,
1000, etc. in its denominator. For example.
- 1/2 = 5/10
- 3/4 = 75/100
- 5/8 = 625/1000
Quick Review “Cloning”
fractions
Two fractions are clones if they are equivalent. For example,
1/2 is the clone of 5/10. Why? If you multiply numerator and
denominator by the same number you have a cloned or equivalent
fraction.
Another way to write fractions that have 10,
100, 1000, etc in the denominator is to write it in decimal
notation.
- 75/100 is read “seventy five hundredths”
and equals .75
(BTW - If you say .75 with meaning, you say “75
hundredths”, not “point 75”)
Terminating and Repeating Decimals
Terminating decimals are decimals that do not continue and
end in 00000... after some number(s) after the decimal place.
Some fractions are not as nice. They have numbers that repeat in
their decimal expression. These numbers are known as repeating
decimals.
For example, 1/3 can’t be cloned to have 10, 100, 1000,
etc. in its denominator. Why? Because you can’t come up with a
whole number to clone with for 3 since 3 does not divide into 10,
100, 1000, etc. evenly.
So the best we can do is to treat 1/3 as a
division problem (which it is) and do the division:
0.3333333
3 | 1.0000000
1/3 = 0.3333333......
Here 3 is the repeating number.
Some fractions repeat more than 1 number.
For example, try 1/11:
You should see that 0 and 9 repeat.
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