Write 0.41̅6 as a fraction in its simplest form - OCR - GCSE Maths - Question 18 - 2020 - Paper 6

To remove the repeating part, multiply x by 1000 (to shift the decimal three places right), giving:

$1000x = 416.161616...$

Next, multiply x by 10 to shift it once:

$10x = 4.161616...$

Now, subtract the second equation from the first:

$1000x - 10x = 416.161616... - 4.161616...$

This simplifies to:

$990x = 412$

Now, isolate x:

$x = \frac{412}{990}$

To find the simplest form, divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 412 and 990 is 2:

$x = \frac{212}{495}$

Thus, the answer is:

0.41̅6 = \frac{212}{495}