8.125 as a fraction in simplest form

8.125 as a fraction in simplest form

The correct Answer and Explanation is:

To convert 8.125 into a fraction in simplest form, follow these steps:

Step 1: Express the decimal as a fraction

First, recognize that 8.125 can be written as the sum of a whole number and a decimal:8.125=8+0.1258.125 = 8 + 0.1258.125=8+0.125

Now, we will convert 0.125 into a fraction.

Step 2: Convert the decimal part (0.125) to a fraction

0.125 is a decimal, which is equivalent to 125/1000, since it has three decimal places:0.125=12510000.125 = \frac{125}{1000}0.125=1000125​

Step 3: Simplify the fraction

Next, simplify 1251000\frac{125}{1000}1000125​. Find the greatest common divisor (GCD) of 125 and 1000. The GCD is 125. Divide both the numerator and the denominator by their GCD:125÷1251000÷125=18\frac{125 \div 125}{1000 \div 125} = \frac{1}{8}1000÷125125÷125​=81​

Thus, 0.125=180.125 = \frac{1}{8}0.125=81​.

Step 4: Add the whole number and the fraction

Now, add the whole number (8) to the fraction 18\frac{1}{8}81​. To do this, express 8 as a fraction with the same denominator (8):8=8×88=6488 = \frac{8 \times 8}{8} = \frac{64}{8}8=88×8​=864​

Now, add the two fractions:648+18=658\frac{64}{8} + \frac{1}{8} = \frac{65}{8}864​+81​=865​

Step 5: The final fraction

Thus, 8.125 as a fraction in simplest form is:8.125=6588.125 = \frac{65}{8}8.125=865​

Explanation:

When converting a decimal to a fraction, you first separate the whole number from the decimal part. In this case, 8.125 is broken into 8 and 0.125. You then convert the decimal part to a fraction by placing it over a power of 10 (depending on the number of decimal places), simplify it, and finally combine it with the whole number. This step-by-step method ensures accuracy in representing decimals as fractions. The key is simplifying the fraction by using the greatest common divisor, which results in the simplest form.