Convert the decimal to a fraction.
0.273 repeated
273/ 1000 + 273/ 1,000,000 + ....
273 [ 1/10^3 + 1/10^6 + 1/10^9 ....
each term is 10^-3 times the previous one.
Look familiar ?
To convert a repeating decimal to a fraction, you can use the concept of geometric series. In this case, the number 0.273 repeated can be expressed as:
x = 0.273273273...
Next, let's multiply this number by a power of 10 to eliminate the repeating part.
10x = 2.732732732...
Subtracting the original equation from the above equation will eliminate the repeating part:
10x - x = 2.732732732... - 0.273273273...
Simplifying the equation:
9x = 2.459
Now, we can solve for x by dividing both sides of the equation by 9:
x = 2.459 / 9
This gives you the fraction representation of the decimal:
x = 0.273273273... = 2.459 / 9
To further simplify this fraction, you can divide both the numerator and denominator by their greatest common divisor (GCD), which is 1 in this case.
Therefore, the simplified fraction representation of 0.273 repeated is:
2.459/9