The decimal equivalent of $\frac{7}{8}$ is $0.875$.
To convert the fraction $\frac{7}{8}$ to a decimal, we can use long division.
Set up the division: Write 7 as the dividend inside the division bracket and 8 as the divisor outside the bracket. Since 7 is less than 8, we need to add a decimal point and zeros to the dividend.
Add a decimal point and zero: Place a decimal point in the quotient (the answer) directly above the decimal point in the dividend. Then, add a zero to the right of 7, making it 70.
Divide: Determine how many times 8 goes into 70. The answer is 8 times, which gives us 64.
Subtract: Subtract 64 from 70 to get the remainder, which is 6.
Add another zero and continue dividing: Since there is a remainder, add another zero to bring down, making it 60.
Repeat the division: Now, determine how many times 8 goes into 60. The answer is 7 times, which gives us 56.
Subtract again: Subtract 56 from 60 to get the remainder, which is 4.
Add another zero if necessary: Since there is still a remainder, add another zero to bring down, making it 40.
Final division: Determine how many times 8 goes into 40. The answer is 5 times, with no remainder.
To check if the answer is correct, we can multiply the decimal by the denominator of the original fraction:
$0.875 \times 8 = 7$
Since the result is the numerator of the original fraction, our conversion is correct.
Converting a fraction to a decimal involves dividing the numerator by the denominator. If the division doesn't come out evenly, you continue by adding zeros to the right of the dividend and bringing them down one at a time until you can divide evenly or until you reach the desired number of decimal places. The quotient you obtain is the decimal equivalent of the original fraction. This process is useful in many areas of mathematics and everyday life, as decimals are often easier to work with than fractions.