How do I convert this decimal into a fraction?
3.083 (The last 3 is repeating by itself)
let x = 3.0833333..
times 10
10x = 30.833333...
x = 3.083333..
subtract them:
9x = 27.75
x = 27.75/9 = 2775/900 = 37/12
we all know that 1/12 = 0.083333
So, we have 3 1/12 = 37/12
we do all know common fractions as decimals, don't we? :-)
How did you do it? :)
Thanks so much #yolo
To convert a decimal into a fraction, follow these steps:
Step 1: Let x be the given decimal number without the repeating part. In this case, x = 3.08.
Step 2: Count the number of decimal places in the given number. In this case, there are two decimal places.
Step 3: Multiply the given decimal by a power of 10, where the power is equal to the number of decimal places. In this case, multiply 3.08 by 100 to remove the decimal places:
3.08 * 100 = 308.
Step 4: Let y be the number obtained in step 3. In this case, y = 308.
Step 5: Subtract the value obtained in step 1 from the value obtained in step 4. In this case, 308 - 3.08 = 304.92.
Step 6: Set up an equation where the repeating part is represented by x:
10^kx = y, where k is the number of repeating digits (in this case, k = 1) and y is the non-repeating part of the number.
Step 7: Solve for x:
10^kx = y
10^1x = 304.92
10x = 304.92
Step 8: Solve for x by dividing both sides of the equation by 10:
x = 304.92 / 10
x = 30.492
Step 9: Convert x into a fraction by putting it over a power of 10, where the power is the number of decimal places in x:
x = 30.492 / 100
Step 10: Simplify the fraction if possible:
x = 30.492 / 100 = 30492 / 1000
Final Answer: The decimal 3.083 (with the last 3 repeating) can be expressed as the fraction 30492/1000.
1 8333/1000
so you have 3.0833333....
quick way
= 3 + .083333...
= 3 + (83-8)/900
= 3 + 75/900
= 3 + 1/12
= 37/12
check by dividing 37 by 12 = 3.083333...