Convert 0.86 into a fraction reduce to 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 can follow these steps:
Step 1: Write the Decimal as a Fraction
The decimal 0.86 can be expressed as a fraction with 86 as the numerator and 100 as the denominator, since there are two decimal places:
[
0.86 = \frac{86}{100}
]
Step 2: Reduce the Fraction
Next, we need to reduce the fraction (\frac{86}{100}) to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator and denominator.
- Finding the GCD: The prime factorization of 86 is:
- 86 = 2 × 43 (both 2 and 43 are prime numbers) The prime factorization of 100 is:
- 100 = 2 × 2 × 5 × 5 = (2^2 \times 5^2)
Now, we can see that the GCD of 86 and 100 is 2 (the only common factor).
Step 3: Divide the Numerator and Denominator by the GCD
To reduce the fraction, we divide both the numerator and the denominator by their GCD:
[
\frac{86 \div 2}{100 \div 2} = \frac{43}{50}
]
Step 4: Conclusion
Thus, the decimal 0.86 as a fraction in its lowest terms is:
[
\frac{43}{50}
]
Explanation
This process illustrates how to convert a decimal to a fraction and then simplify it. Understanding these steps is essential in various fields, such as mathematics, finance, and even everyday scenarios where precision is required. Being able to manipulate decimals and fractions is particularly useful in contexts like nursing, where medication dosages may need to be calculated accurately. Converting decimals to fractions can also help in understanding ratios and proportions, which are critical for interpreting data effectively. Hence, mastering these conversions enhances numerical literacy and practical skills in various professional fields.