Question

Please help ASAP!

Write the recurring decimal 0.123 (1 and 3 being the repeated) as a fraction

Answer 1

The simplest exact fraction for the decimal number 0.123 is 1231000

Answer 2

The recurring decimal 0.123 (1 and 3 being the repeated) can be expressed as the fraction 41/333.

To express the recurring decimal 0.123 (1 and 3 being the repeated) as a fraction, we use algebraic methods. Let x = 0.123(13). Multiplying both sides by 1000 eliminates the recurring part:

1000x = 123.131313...

Subtracting the original equation from this new one eliminates the recurring decimal:

1000x - x = 123.131313... - 0.1231313...

This simplifies to 999x = 123. Solving for x:

x = 123/999.

Further simplifying by finding the greatest common factor (GCF) of the numerator and denominator, which is 3:

x = 41/333.

So, 0.123 (1 and 3 being the repeated) as a fraction is 41/333.