Consider the repeating decimal 0.451414141414...... Prove that this number is rational by converting it into a fraction of two integers. You do NOT need to reduce the fraction.

Answer 1

.45141414...=.45 + x

.00141414..= x

100x = .141414....

100x-x = .14

99x = .14/99 = 14/9900

.45141414...= .45 + .00141414...

= 45/100 + 14/9900

= (45(99)+14)/9900

= 4469/9900

check the answer with a calculator

plug n 4469 and divide by 9900

you get .45141414....

any repeating decimal is a rational number