Question

What fractions are equal to 17.09 repeating

Answer 1

The repeating decimal 17.09 (with 09 repeating) can be expressed as the fraction 1692/99 after using an algebraic method to remove the repeater and simplify the fraction.

Step-by-step explanation:

The number 17.09 where 09 is repeating can be written as a fraction by using algebraic methods to convert it from a decimal to a fraction. The steps are as follows:

1. Let x represent the repeating decimal 17.09 (with 09 repeating).
2. Since 09 is the repeating part, we need to multiply x by 100 to shift the decimal two places to the right: 100x = 1709.09...
3. Subtract the original equation (x = 17.09...) from this new equation to get rid of the repeating part: 100x - x = 1709.09... - 17.09...
4. The subtraction gives us 99x = 1692 because the repeating decimals cancel each other out.
5. Divide both sides by 99 to solve for x: x = 1692/99.
6. Simplify the fraction to its lowest terms, if necessary.

The fraction that represents the repeating decimal 17.09 (with 09 repeating) is 1692/99.

Answer 2

17.09 has 2 decimal places, so we put the decimal digits of 17.09, 09, over 1 followed by the number of zeroes equal to the number of decimal places, 2: 09 = 09/100. We add 17 as 1700/100 and get: 17.09 as decimal fraction = 1709/100