express the repeating decimal 10.232323 as a ratio of two integers
10 23/99
I do this by taking the 23/100 and subtracting 1 from the denominator to get 23/99.
If you had 10.33333
I would put 3/10 minus 1 from denominator to get 3/9 or 1/3.
To express the repeating decimal 10.232323 as a ratio of two integers, we can follow these steps:
Step 1: Let x be the repeating decimal.
x = 10.232323...
Step 2: Multiply both sides of the equation by a power of 10 to eliminate the repeating part. Since there are two digits repeating, we multiply by 100:
100x = 1023.232323...
Step 3: Subtract the original equation from the one obtained in Step 2:
100x - x = 1023.232323... - 10.232323...
99x = 1013
Step 4: Divide both sides of the equation by 99 to solve for x:
x = 1013/99
Therefore, the repeating decimal 10.232323 can be expressed as the ratio of two integers: 1013/99.
To express the repeating decimal 10.232323 as a ratio of two integers, we can follow these steps:
Step 1: Let x be the repeating decimal.
x = 10.2323...
Step 2: Multiply both sides of the equation by a power of 10 to shift the repeating part to the left of the decimal point. Since there are two digits repeating, we multiply by 100:
100x = 1023.2323...
Step 3: Subtract the original equation from the one obtained in step 2 to eliminate the repeating part:
100x - x = 1023.2323... - 10.2323...
Simplifying:
99x = 1013 (since 1023 - 10 = 1013)
Step 4: Divide both sides of the equation by 99 to isolate x:
x = 1013/99
Thus, the repeating decimal 10.232323 can be expressed as the ratio 1013/99.