Write the repeating decimal <span title="0.351351351351351351351...">0.351351351351351351351.....</span> as a reduced fraction.?

Question

Write the repeating decimal 0.351351351351351351351..... as a reduced fraction.?

Answer 1

Here&#039;s how to convert 0.351351351351351 to a fraction...

The decimal part of your number seems to have the digits 351 repeating in it.

Your original number to convert is 0.351351. Let&#039;s slide the decimal point in this number to the right 3 place(s) (the same number of digits in the number 351).

If we do this, we&#039;ll get a 351.351351 (slide the decimal in the 0.351351 right 3 places, you&#039;ll get 351.351351).

So what? Well now, we have two numbers with the same repeating decimal parts, 351.351351 and 0.351351.

Now let&#039;s just work a little algebra into all of this. Let&#039;s call your original number x. And in this case, x=0.351351. The number with the decimal point slid over can be called 1000x, because 1000x=351.351351

What if we subtracted these two equations (that is, subtract the items on the left of the equal sign

from the stuff on the right of the equal sign)?

1000x = 351.351- x = 0.351351---------------999x = 351.

Now here&#039;s the important result of doing all of this: Notice how all of the repeating decimal parts have subtracted away to zero! We are left with a nice, simple 351 on the right side of the equal sign.

Now, solving 999x=351 for x by dividing both sides of it by 999, we&#039;ll get that x=351/999. And this is your answer.

How is this your answer? Well remember that above, x was originally set equal to 0.351351 via x=0.351351, and now we have that x is also equal to 351/999, so that means 0.351351=351/999..and there&#039;s 0.351351 written as a fraction!

The fraction is not reduced to lowest terms. We can reduce this fraction to lowest

terms by dividing both the numerator and denominator by 27.

Why divide by 27? 27 is the Greatest Common Divisor (GCD)

or Greatest Common Factor (GCF) of the numbers 351 and 999.

So, this fraction reduced to lowest terms is 13/27

So your final answer is: 0.351351351 can be written as the fraction

13/37

Answer 2

1.35

Answer 3

let x= 0.351351351351351351351.

multiply by 1000

1000x= 351.351351351351351351.

now subtract the 2 lines

999x = 351

so x = 351/999

x = 117/333 =13/37

Answer 4

.351351....

=351/1000+351/1000000+.....

=(351/1000)/)(1-1/1000) GEOMETRIC SERIES

with r=1/1000, a=351/1000

=(351/1000)/(999/1000)

=351/999

=117/333

=39/111

=13/37

Answer 5

351/999

= 13/37

Answer 6

351/999 = 117/333 = 39/111 = 13/37

Answer 7

0.351(bar notation over 351) = 351 over 999(you can&#039;t reduce it more than that)