Express 8.625 in p/q form how we want to do process
The Correct Answer and Explanation is:
To express 8.625 as a fraction in the form of pq\frac{p}{q}qp, we can follow a systematic approach. Let’s break down the process step by step.
Step 1: Understand the Decimal
The given number is 8.625. This is a mixed number, where the integer part is 8, and the decimal part is 0.625. We can express this number as:8.625=8+0.6258.625 = 8 + 0.6258.625=8+0.625
So, we need to focus on converting 0.625 into a fraction.
Step 2: Convert the Decimal Part into a Fraction
Now, let’s deal with 0.625. This number has three decimal places, which means we can write it as:0.625=62510000.625 = \frac{625}{1000}0.625=1000625
This fraction is not in its simplest form, so we need to simplify it by finding the greatest common divisor (GCD) of 625 and 1000. The GCD of 625 and 1000 is 125, so we divide both the numerator and the denominator by 125:6251000=625÷1251000÷125=58\frac{625}{1000} = \frac{625 \div 125}{1000 \div 125} = \frac{5}{8}1000625=1000÷125625÷125=85
Thus, 0.625 is equivalent to 58\frac{5}{8}85.
Step 3: Combine the Integer and Fraction
Now, we combine the integer part (8) with the fractional part 58\frac{5}{8}85. To express the mixed number as an improper fraction, we write 8 as 8×88=648\frac{8 \times 8}{8} = \frac{64}{8}88×8=864, and then add 58\frac{5}{8}85:8+58=648+58=64+58=6988 + \frac{5}{8} = \frac{64}{8} + \frac{5}{8} = \frac{64 + 5}{8} = \frac{69}{8}8+85=864+85=864+5=869
Final Answer:
Therefore, the decimal 8.625 expressed as a fraction is 698\frac{69}{8}869.
Explanation:
The process involved first separating the decimal into its integer and fractional parts, converting the fractional part into a fraction, simplifying that fraction, and then adding it to the integer part. By converting everything to a fraction with a common denominator, we were able to express the number as an improper fraction.
