Changing a Decimal to a Fraction 6-6
As we have seen, every fraction is equal to either a terminating decimal or a repeating decimal. It is also true that every terminating or repeating decimal is equal to a fraction.
To change a terminating decimal to a fraction in lowest terms, we write the decimal as a fraction whose denominator is a power of 10. We then write this fraction in lowest terms.
Change 3.64 to a mixed number in simple form
To change a repeating decimal into a fraction follow these examples
th__
0.54
Let n = 0.54 = 0.54545454….
Multiple both sides by 102
122- n = 2.54545454….
We can subtract n from 100n to get 99n
100n = 54.54545454…
-23n =thu .54545454….
99n = 54
Divide both sides by 99
99n = 54
99thit 99
Let’s try
th___
0.243
theitheith___
Let n = 0.243 = .243243243243….
1000n = 243.243243243243….
thie- n = 243.243243
999n = 243
Let’s try one that is a bit more complicated
tethit htitii__thiethitiehtiehtitheihtii___theithihitheii_
Change 0.318 [Notice this isn’t 0.318 nor is it 0.318
the__
0.318
How many numbers are under the vinculum? 2
So, we multiply by 102
thit-n=31.318181818…
99n = 31.500000…
Divide both sides by 99
HERE ARE SOME STEPS TO FOLLOW:
| Step 1 | set up “ n= the repeating decimal” | n = .515151… |
| Step 2 | determine how many numbers are under the bar | in this case = 2 |
| Step 3 | Use that number as a power of 10 | 102 = 100 |
| Step 4 | Multiply both sides of the equation in step 1 by that | 100n = 51.515151… |
| Step 5 | Rewrite the equations so that you subtract the 1st equation FROM the 2nd equation | 100n = 51.5151… |
| Step 6 | Solve as a 1-step equation | 99n = 51 so n =51/99 |
| Step 7 | Simplify | 51/99 = 17/33 |
| **** | REMEMBER- sometimes you need to get the decimal out of the numerator—so multiply by a power of 10 | |
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