Put the steps in order for changing the repeating decimal, which is rational, to a ratio or fraction. 0.474747.... = what fraction?
1. Let x be the repeating decimal, in this case, 0.474747....
2. Multiply x by a power of 10 to move the decimal point after the repeating block. For example, if the block has n digits, multiply x by 10^n.
3. Subtract x from the result obtained in step 2 to eliminate the repeating part. Let's call this new number y.
4. Determine the number of digits in the repeating block, let's call it n.
5. Multiply y by 10^n to move the decimal point after the repeating block again.
6. Subtract y from the result obtained in step 5 to eliminate the non-repeating part. Let's call this new number z.
7. Determine the number of nines equal to the recurring block. For example, if the repeating block has two digits, the number of nines is 99.
8. Divide z by the number of nines obtained in step 7.
9. Simplify the resulting fraction if possible.
10. The final fraction is the ratio or fraction equivalent of the repeating decimal.
can you put it in 5 steps?
Certainly! Here are the 5 steps to convert a repeating decimal to a fraction:
1. Identify the repeating part of the decimal and assign it a variable, let's call it x.
2. Set up an equation to represent the repeating decimal as a fraction. For example, if the repeating decimal is 0.474747..., you would write: x = 0.474747...
3. Multiply both sides of the equation by a power of 10 so that the decimal point is just after the repeating block. In this case, multiply both sides by 100, since there are two digits in the repeating block: 100x = 47.474747...
4. Subtract the original equation from the equation obtained in step 3 to eliminate the repeating part. In this case, subtract x from 100x to get: 100x - x = 47.474747... - 0.474747..., resulting in 99x = 47.
5. Solve for x by dividing both sides of the equation by 99: x = 47/99.
Therefore, the fraction equivalent of the repeating decimal 0.474747... is 47/99.