Question

Heather was writing the decimal 0.12¯¯¯¯ as a fraction. She worked out the problem, but her fraction is not correct. Where did she make a mistake?

Equation 1: x = 0.12¯¯¯¯
Equation 2: 10x = 12.12¯¯¯¯


10x = 12.12¯¯¯¯
- x = 0.12¯¯¯¯
_______________

9x = 12
x = 12/9=4/3
Question 4 options:

She wrote equation 1 incorrectly.


She multiplied by the wrong power of 10 when setting up equation 2.


She subtracted the two equations incorrectly.


She simplified her fraction incorrectly.

Answer 1

She multiplied by the wrong power of 10 when setting up equation 2.

Explanation:

10*0.121212....=1.212121...., not 12.121212... because when multiplying by 10 you only need to shift the decimal to the right once, not twice.