Convert 0.86 into a fraction and reduce the answer to the lowest terms.
The Correct Answer and Explanation is :
To convert the decimal 0.86 into a fraction and reduce it to its lowest terms, we follow a systematic approach.
Step 1: Understanding the Decimal
The decimal 0.86 means “86 hundredths,” which can be expressed as:
[
0.86 = \frac{86}{100}
]
Step 2: Simplifying the Fraction
Now, we need to simplify the fraction (\frac{86}{100}). Simplifying a fraction involves dividing both the numerator and the denominator by their greatest common divisor (GCD).
Step 3: Finding the GCD
To find the GCD of 86 and 100, we can list the factors of each number:
- Factors of 86: 1, 2, 43, 86
- Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100
The common factors are 1 and 2. The greatest of these is 2, so:
[
\text{GCD}(86, 100) = 2
]
Step 4: Dividing by the GCD
Now, we divide both the numerator and the denominator by the GCD:
[
\frac{86 \div 2}{100 \div 2} = \frac{43}{50}
]
Step 5: Final Result
The fraction (\frac{43}{50}) is in its lowest terms because 43 is a prime number, and it does not share any factors with 50 other than 1.
Summary
To summarize, we converted the decimal 0.86 into the fraction (\frac{86}{100}), found the GCD to be 2, and then simplified the fraction to (\frac{43}{50}). This method of conversion and simplification is crucial in mathematics, as it allows us to express decimal values as exact fractions, providing greater precision in calculations and ensuring clarity in representation. Understanding how to perform these conversions enhances numerical literacy and facilitates various mathematical operations, including addition, subtraction, and comparison of fractions and decimals. The final answer, (\frac{43}{50}), effectively represents the original decimal value in a simplified form.