What is the equivalent of 0.86 when converted to a fraction and reduced to the lowest terms?
Answer (2)
Convert the decimal 0.86 to a fraction: 100 86 .
Find the greatest common divisor (GCD) of 86 and 100, which is 2.
Divide both the numerator and the denominator by the GCD: 100 ÷ 2 86 ÷ 2 = 50 43 .
The simplified fraction is 50 43 .
Explanation
Understanding the Problem We need to convert the decimal 0.86 into a fraction and then simplify it to its lowest terms.
Converting to a Fraction First, we express 0.86 as a fraction. Since 0.86 has two decimal places, we can write it as 100 86 .
Finding the GCD Next, we need to simplify the fraction 100 86 to its lowest terms. To do this, we find the greatest common divisor (GCD) of the numerator (86) and the denominator (100).
GCD Calculation The greatest common divisor (GCD) of 86 and 100 is 2. This means that 2 is the largest number that divides both 86 and 100 without leaving a remainder.
Simplifying the Fraction Now, we divide both the numerator and the denominator by their GCD, which is 2. 100 ÷ 2 86 ÷ 2 = 50 43
Final Answer The fraction 50 43 is now in its simplest form because 43 is a prime number, and it does not divide 50. Therefore, the equivalent of 0.86 when converted to a fraction and reduced to the lowest terms is 50 43 .
Examples
In construction, you might need to convert decimal measurements to fractions for ease of use with traditional measuring tools. For example, if a measurement is 0.86 inches, converting it to the fraction 50 43 inches allows for more precise marking and cutting using a ruler or other measuring devices that are graduated in fractions of an inch. This ensures accuracy in fitting materials together.
The decimal 0.86 can be converted to the fraction 100 86 . Simplifying this by dividing the numerator and denominator by their GCD (2) results in 50 43 . Therefore, the lowest terms of 0.86 as a fraction is 50 43 .
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