Write the following decimal numbers as fractions. 0.111
The Correct Answer and Explanation is:
To convert the decimal (0.111) into a fraction, let’s go through the process step-by-step.
Step 1: Understand the Decimal Structure
The decimal (0.111) can be written as:
[
0.111 = \frac{111}{1000}
]
This is because the digit (111) is in the thousandths place. The thousandths place is three places to the right of the decimal point, so we multiply (111) by (10^3 = 1000) to convert the decimal to a fraction.
Step 2: Write the Decimal as a Fraction
Since (0.111) has three decimal places, we write it as:
[
0.111 = \frac{111}{1000}
]
Step 3: Simplify the Fraction (if needed)
Now, we check whether the fraction can be simplified. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and denominator. The numerator is (111), and the denominator is (1000).
We first find the factors of both numbers:
- Factors of (111): (1, 3, 37, 111)
- Factors of (1000): (1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000)
The only common factor between (111) and (1000) is (1), meaning the greatest common divisor (GCD) is (1). Therefore, the fraction is already in its simplest form.
Step 4: Conclusion
So, the decimal (0.111) can be written as the fraction:
[
\frac{111}{1000}
]
Since the GCD is (1), the fraction cannot be simplified further. Therefore, (0.111) as a fraction is (\frac{111}{1000}).
Explanation Recap:
- Start by recognizing that (0.111) has three decimal places, so it’s equivalent to (\frac{111}{1000}).
- Check for the greatest common divisor (GCD) between the numerator and denominator.
- Since the GCD is (1), the fraction is already in its simplest form.
- The final fraction representation of (0.111) is (\frac{111}{1000}).