To convert the repeating decimal 0.09 repeating to a rational number, we can represent it as a fraction by setting it equal to a variable, let's say x:
x = 0.0999999...
Next, multiply both sides of the equation by 100 to shift the decimal point two places to the right:
100x = 9.99999...
Now, subtract the original equation from the new equation to eliminate the repeating decimal:
100x - x = 9.99999... - 0.099999...
99x = 9.9
Divide both sides of the equation by 99 to solve for x:
x = 9.9/99
Simplifying the numerator and denominator:
x = 1/10
Therefore, 0.09 repeating as a rational number in simplest form is 1/10.
Convert 0.09 repeating to a rational number in simplest form.(1 point) Responses 9100 9 over 100 19 1 ninth 910 9 tenths 111
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