Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.171717.... = what fraction?
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1.x = 17/00
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2.subtract (x = 0.171717....)
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3.100x = 17.1717....
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4.x = 0.171717
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5.99x = 17
1. x = 0.171717....
2. Multiply both sides by 100 to eliminate the repeating decimal: 100x = 17.1717....
3. Subtract x from both sides: 99x = 17
4. Divide both sides by 99: x = 17/99
So, the fraction 0.171717.... is equal to 17/99.
Here are the steps in order for changing the repeating decimal 0.171717... to a fraction or ratio:
1. x = 0.171717...
2. Multiply both sides of the equation by 100 to move the decimal point two places to the right:
100x = 17.171717...
3. Subtract the original equation from the equation obtained in step 2:
100x - x = 17.171717... - 0.171717...
4. Simplify the equation:
99x = 17
5. Divide both sides of the equation by 99 to solve for x:
x = 17/99
Therefore, the fraction equivalent of the repeating decimal 0.171717... is 17/99.
To change a repeating decimal to a fraction, follow these steps:
1. Let x be the repeating decimal.
2. Multiply both sides of the equation x = 0.171717... by an appropriate power of 10 to get rid of the repeating part. In this case, multiply by 100.
Result: 100x = 17.171717...
3. Subtract the original equation from the equation obtained in step 2 to eliminate the repeating part:
100x - x = 17.171717... - 0.171717...
Simplify:
99x = 17
4. Solve for x by dividing both sides of the equation by 99:
x = 17/99
Therefore, 0.171717... is equal to the fraction 17/99.
100 • 0.1717... = 17.1717...
100 • 0.1717... - 0.1717... = 17.1717... - 0.1717...
99 • 0.1717... = 17
0.1717... = 17 / 99