Answer: 1.3415 as a fraction is 6707.5/5000
Converting the decimal number 1.3415 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 1.3415 can be broken down as:
1.3415 = 1 + 0.3415
Here, 1 is the whole number part, and 0.3415 is the decimal part.
Focus on converting the decimal part, 0.3415, to a fraction. To do this, consider the place value of the decimal:
0.3415 =
3415
10000
Now, simplify the fraction 3415/10000. To do this, find the greatest common divisor (GCD) of 3415 and 10000.
Now, divide both the numerator and the denominator by their GCD:
3415 ÷ 2
10000 ÷ 2
=
1707.5
5000
So, 0.3415 as a fraction is 1707.5/5000
Now that you have 1.3415 = 1 + 0.3415, express the entire number as a mixed fraction:
1.3415
= 1 +
1707.5
5000
=
5000
5000
+
1707.5
5000
=
6707.5
5000
Here, 5000/5000 is the whole number 1, and 1707.5/5000 is the fractional part.
Answer: 1.3415 = 6707.5/5000
Converting 1.3415 to a fraction results in 6707.5/5000. 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.