Answer: 0.8640 as a fraction is 108/125
Converting the decimal number 0.8640 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 0.8640 can be broken down as:
0.8640 = 0 + 0.864
Here, 0 is the whole number part, and 0.864 is the decimal part.
Focus on converting the decimal part, 0.864, to a fraction. To do this, consider the place value of the decimal:
0.864 =
864
1000
Now, simplify the fraction 864/1000. To do this, find the greatest common divisor (GCD) of 864 and 1000.
Now, divide both the numerator and the denominator by their GCD:
864 ÷ 8
1000 ÷ 8
=
108
125
So, 0.864 as a fraction is 108/125
Now that you have 0.8640 = 0 + 0.864, express the entire number as a mixed fraction:
0.8640
= 0 +
108
125
=
0
125
+
108
125
=
108
125
Here, 0/125 is the whole number 0, and 108/125 is the fractional part.
Answer: 0.8640 = 108/125
Converting 0.8640 to a fraction results in 108/125. 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.