Question

Using complete sentences, explain how to convert 0.17 repeating to a tion.

Answer 1

To convert the repeating decimal 0.17 to a fraction, set it equal to x, multiply by 10, subtract the original x from this result, solve for x, and simplify the resulting fraction to get 4/45.

Step-by-step explanation:

Converting a repeating decimal to a fraction involves some algebraic manipulation. Let's convert the repeating decimal 0.17 (where 7 is repeating) to a fraction.

1. Let x equal the repeating decimal, so x = 0.177...
2. Multiply x by 10 to shift the decimal point to the right, so 10x = 1.777... Since our repeating part is the digit 7, we need a power of 10 that shifts the whole repeating section.
3. Subtract the original x from 10x to get 9x, which eliminates the repeating part: 10x - x = 1.777... - 0.177... = 1.6
4. So now we have 9x = 1.6, and to find x, divide both sides by 9: x = 1.6 / 9
5. Finally, convert the decimal 1.6 to a fraction, which is 16/10, and simplify if needed. So we have x = (16/10) / 9 = 16/(10*9) = 16/90. The fraction can be simplified to 4/45. Therefore, 0.177... as a fraction is 4/45.