Convert the decimal 0.625 into a fraction.
A) 5/8
B) 3/4
C) 2/5
D) 4/5
The Correct Answer and Explanation is:
To convert the decimal 0.625 into a fraction, follow these steps:
Step 1: Understand the Decimal
The number 0.625 is a decimal with three digits after the decimal point. This indicates it is in the thousandths place, as there are three digits after the decimal point.
Step 2: Express the Decimal as a Fraction
To convert 0.625 into a fraction, we can write it as:
[
\frac{625}{1000}
]
This means 0.625 is the same as 625 thousandths. The next step is to simplify this fraction by finding the greatest common divisor (GCD) of 625 and 1000.
Step 3: Simplify the Fraction
We need to simplify (\frac{625}{1000}) by dividing both the numerator (625) and the denominator (1000) by their GCD. To find the GCD of 625 and 1000, we begin by factoring each number.
- 625 factors as: ( 625 = 5^4 )
- 1000 factors as: ( 1000 = 2^3 \times 5^3 )
The common factors between 625 and 1000 are powers of 5, specifically (5^3 = 125). Therefore, the GCD of 625 and 1000 is 125.
Step 4: Divide Both the Numerator and Denominator by the GCD
Now, divide both the numerator and the denominator of (\frac{625}{1000}) by 125:
[
\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
]
Step 5: Conclusion
After simplifying, we find that 0.625 is equivalent to the fraction (\frac{5}{8}).
Thus, the correct answer is A) 5/8.
Explanation of the Options:
- A) 5/8: This is the correct simplified fraction.
- B) 3/4: This fraction is larger than 0.625, as 3 divided by 4 equals 0.75.
- C) 2/5: This fraction equals 0.4, which is less than 0.625.
- D) 4/5: This fraction equals 0.8, which is greater than 0.625.
Therefore, the correct fraction representation of 0.625 is 5/8.