Convert the decimal to a fraction in simplest form: 0.0625 =
The Correct Answer and Explanation is:
Correct Answer: 0.0625=1160.0625 = \frac{1}{16}0.0625=161
Explanation:
To convert the decimal 0.0625 into a fraction in simplest form, we follow a few clear steps.
Step 1: Understand Place Value
The decimal 0.0625 means 625 ten-thousandths (because the last digit, 5, is in the ten-thousandths place).
So we can first write: 0.0625=62510,0000.0625 = \frac{625}{10,000}0.0625=10,000625
Step 2: Simplify the Fraction
Now, simplify the fraction 625/10,000 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
Let’s find the GCD of 625 and 10,000:
- 625 ÷ 125 = 5
- 10,000 ÷ 125 = 80
So, 62510,000=580\frac{625}{10,000} = \frac{5}{80}10,000625=805
Now simplify 5/80 further:
- 5 ÷ 5 = 1
- 80 ÷ 5 = 16
Therefore: 580=116\frac{5}{80} = \frac{1}{16}805=161
So, 0.0625=1160.0625 = \frac{1}{16}0.0625=161
Alternative Method: Using Powers of 10
Since 0.0625 is a terminating decimal, we can also convert it using place values: 0.0625=62510,0000.0625 = \frac{625}{10,000}0.0625=10,000625
This is the same fraction as before, and simplifies to 1/16.
Conclusion:
The decimal 0.0625 equals the fraction 1/16 in simplest form. This conversion shows how understanding place value and simplifying fractions using the greatest common divisor helps translate decimals into clean, exact fractions. This skill is especially useful in nursing, science, and other fields that require precise measurement and interpretation of numerical data.
