Convert the recurring decimal to a fraction
0.915915
0.317317
just divide by 10 to the (length of repeating part) power:
915/1000
317/1000
and the reduce the fraction if possible
0.215
To convert a recurring decimal to a fraction, we have to identify the pattern and express it in terms of fractions.
For the recurring decimal 0.915915:
1. Let x = 0.915915.
2. Multiply x by a power of 10 to remove the decimal part. In this case, we have three recurring digits, so multiply x by 1000:
1000x = 915.915915.
3. Subtract the original equation from the one obtained in the previous step:
1000x - x = 915.915915 - 0.915915:
999x = 915.
4. Divide both sides of the equation by 999 to solve for x:
x = 915 / 999.
Therefore, the fraction representation of the recurring decimal 0.915915 is 915/999.
Similarly, for the recurring decimal 0.317317:
1. Let x = 0.317317.
2. Multiply x by a power of 10 to remove the decimal part. In this case, we have three recurring digits, so multiply x by 1000:
1000x = 317.317317.
3. Subtract the original equation from the one obtained in the previous step:
1000x - x = 317.317317 - 0.317317:
999x = 317.
4. Divide both sides of the equation by 999 to solve for x:
x = 317 / 999.
Therefore, the fraction representation of the recurring decimal 0.317317 is 317/999.
To convert a recurring decimal to a fraction, we need to identify the repeating pattern and express it as a fraction.
Let's consider the first example: 0.915915.
Step 1: Identify the repeating pattern
In this case, the pattern is 915.
Step 2: Count the number of digits in the repeating pattern
In this case, there are three digits in the repeating pattern.
Step 3: Create an equation
To convert the repeating decimal to a fraction, we'll create the equation where x is the repeating pattern:
x = 0.915915
Step 4: Multiply the equation by a power of 10
To eliminate the repeating part, we'll multiply the equation by 1000 (10 to the power of 3, as there are three digits in the repeating pattern):
1000x = 915.915
Step 5: Subtract the equation from the multiplied equation
We subtract the original equation from the equation multiplied by 1000 to cancel out the repeating part:
1000x - x = 915.915 - 0.915915
999x = 915
Step 6: Solve for x
Divide both sides of the equation by 999 to isolate x:
x = 915 / 999
So, 0.915915 as a fraction is 915/999.
Let's move on to the second example: 0.317317.
Step 1: Identify the repeating pattern
In this case, the pattern is 317.
Step 2: Count the number of digits in the repeating pattern
In this case, there are three digits in the repeating pattern.
Step 3: Create an equation
To convert the repeating decimal to a fraction, we'll create the equation where x is the repeating pattern:
x = 0.317317
Step 4: Multiply the equation by a power of 10
To eliminate the repeating part, we'll multiply the equation by 1000 (10 to the power of 3, as there are three digits in the repeating pattern):
1000x = 317.317
Step 5: Subtract the equation from the multiplied equation
We subtract the original equation from the equation multiplied by 1000 to cancel out the repeating part:
1000x - x = 317.317 - 0.317317
999x = 317
Step 6: Solve for x
Divide both sides of the equation by 999 to isolate x:
x = 317 / 999
So, 0.317317 as a fraction is 317/999.