Express each decimal of integers, in simplest form.

0.1 with the repeating decimal 1

1/9

check with the my reply to Greg at 9:55 above

How to express 0.3 as a quotient of two integers

Why did the math book go to the therapist?

Because it had too many unresolved decimal issues!

To express 0.1 with the repeating decimal 1, we can write it as follows:

0.1 = 0.11111...

To express the repeating decimal 0.1 as an integer in simplest form, we can convert it to a fraction.

Let's denote x = 0.1, then we can rewrite it as x = 0.1111...

To convert this repeating decimal to a fraction, we observe that the repeating pattern occurs after the decimal point. Since there is only one repeating digit, which is 1, it means that the repeating part has a length of 1.

To find the fraction, we multiply both sides of the equation x = 0.1111... by 10, since there is only one repeating digit:

10x = 1.1111...

Now, we subtract the original equation from the new equation to eliminate the repeating part:

10x - x = 1.1111... - 0.1111...
9x = 1

Dividing both sides of the equation by 9 gives us the simplified fraction:

x = 1/9

Therefore, the decimal 0.1, with the repeating decimal 1, can be expressed as the fraction 1/9 in simplest form.