Express 0.625 as a fraction in its lowest term.
The correct answer and explanation is:
Correct Answer: 0.625=580.625 = \frac{5}{8}
Explanation (300 words):
To convert the decimal 0.625 into a fraction and simplify it to its lowest terms, we follow a systematic approach.
Step 1: Understand Place Value
The decimal 0.625 has three digits after the decimal point, which means it is in the thousandths place. So we can write: 0.625=62510000.625 = \frac{625}{1000}
Step 2: Simplify the Fraction
We now simplify the fraction 6251000\frac{625}{1000}. To do this, we divide both the numerator and the denominator by their greatest common divisor (GCD).
We start by finding the GCD of 625 and 1000.
- Factors of 625: 1, 5, 25, 125, 625
- Factors of 1000: 1, 2, 4, 5, 10, 20, 25, 40, 50, 100, 125, 250, 500, 1000
The greatest common divisor of 625 and 1000 is 125.
Now divide both numerator and denominator by 125: 625÷1251000÷125=58\frac{625 \div 125}{1000 \div 125} = \frac{5}{8}
So: 0.625=580.625 = \frac{5}{8}
Step 3: Verify the Answer
To verify, divide 5 by 8: 58=0.625\frac{5}{8} = 0.625
This confirms the conversion is accurate.
Why This Is Useful
Converting decimals to fractions helps in fields like engineering, construction, and finance, where precise ratios are often preferred. Also, fractions can be easier to work with in algebraic operations, such as simplifying expressions or solving equations.
In summary, 0.625 is equivalent to 58\frac{5}{8} in its lowest terms. The process involves recognizing the decimal place value, converting to a fraction, and simplifying using the GCD.