What is the decimal equivalent of 5/8
The Correct Answer and Explanation is :
The decimal equivalent of ( \frac{5}{8} ) is 0.625.
Explanation:
To convert a fraction to its decimal form, you divide the numerator (the number on top) by the denominator (the number on the bottom).
For ( \frac{5}{8} ), the numerator is 5, and the denominator is 8. To convert it into a decimal, we perform the division:
[
5 \div 8 = 0.625
]
Step-by-step division process:
- Start with 5.00 (or 5 with two zeros for precision).
- Divide 50 by 8: The first part is ( 8 ) into 50, which goes 6 times (because 8 × 6 = 48). This gives 6 as the first decimal digit.
- Subtract 48 from 50, leaving a remainder of 2.
- Bring down the next zero, making the number 20.
- Divide 20 by 8: 8 goes into 20 twice (because 8 × 2 = 16). This gives 2 as the next decimal digit.
- Subtract 16 from 20, leaving a remainder of 4.
- Bring down another zero, making it 40.
- Divide 40 by 8: 8 goes into 40 five times (because 8 × 5 = 40). This gives 5 as the final decimal digit.
After the division, we get 0.625.
This result can be checked by multiplying the decimal back by 8 to ensure it gives the original numerator (5):
[
0.625 \times 8 = 5
]
General Rule:
Whenever you divide a number by a power of 10 (like 8 in this case), the division process can be done through long division or by using a calculator, and the result can be written as a decimal. Fractions that cannot be expressed exactly as a finite decimal, such as ( \frac{1}{3} ), will result in repeating decimals, but ( \frac{5}{8} ) is a terminating decimal with a finite number of decimal places (3 digits).