Question

Express the number as a ratio of integers.
0 . 1=0.1111 …

Answer 1

To express the repeating decimal 0.1111… as a ratio of integers, it can be represented as the fraction 1/9.

Step-by-step explanation:

To express the number 0.1111… as a ratio of integers, we use a common mathematical technique that involves setting the number equal to an unknown variable, say x, then creating another equation that removes the repeating decimal part, and finally solving for x to get the ratio.

Let x = 0.1111…

Multiply both sides by 10 to shift the decimal point one place to the right: 10x = 1.1111…

Now, subtract the original equation (x = 0.1111…) from the new equation (10x = 1.1111…):

9x = 1.1111… - 0.1111…

9x = 1

Therefore, x = 1/9

The number 0.1111… can be expressed as the ratio of integers 1/9.