Answer: 0.8660 as a fraction is 433/500
Converting the decimal number 0.8660 into a fraction might seem tricky at first, but with the right steps, it's straightforward. This guide will walk you through the entire process, ensuring you understand each part of the conversion.
The decimal 0.8660 can be broken down as:
0.8660 = 0 + 0.866
Here, 0 is the whole number part, and 0.866 is the decimal part.
Focus on converting the decimal part, 0.866, to a fraction. To do this, consider the place value of the decimal:
0.866 =
866
1000
Now, simplify the fraction 866/1000. To do this, find the greatest common divisor (GCD) of 866 and 1000.
Now, divide both the numerator and the denominator by their GCD:
866 ÷ 2
1000 ÷ 2
=
433
500
So, 0.866 as a fraction is 433/500
Now that you have 0.8660 = 0 + 0.866, express the entire number as a mixed fraction:
0.8660
= 0 +
433
500
=
0
500
+
433
500
=
433
500
Here, 0/500 is the whole number 0, and 433/500 is the fractional part.
Answer: 0.8660 = 433/500
Converting 0.8660 to a fraction results in 433/500. This detailed process of breaking down the decimal, converting it, simplifying, and then combining the parts gives you a clear understanding of how to handle such conversions in math, everyday calculations, or even complex problem-solving.