Answer: 0.1405 as a fraction is 281/2000
Converting the decimal number 0.1405 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.
Step 1: Understand the DecimalThe decimal 0.1405 can be broken down as:
0.1405 = 0 + 0.1405
Here, 0 is the whole number part, and 0.1405 is the decimal part.
Step 2: Convert the Decimal to a FractionFocus on converting the decimal part, 0.1405, to a fraction. To do this, consider the place value of the decimal:
0.1405 =
1405
10000
Now, simplify the fraction 1405/10000. To do this, find the greatest common divisor (GCD) of 1405 and 10000.
Now, divide both the numerator and the denominator by their GCD:
1405 ÷ 5
10000 ÷ 5
=
281
2000
So, 0.1405 as a fraction is 281/2000
Step 4: Combine the Whole Number and FractionNow that you have 0.1405 = 0 + 0.1405, express the entire number as a mixed fraction:
0.1405
= 0 +
281
2000
=
0
2000
+
281
2000
=
281
2000
Here, 0/2000 is the whole number 0, and 281/2000 is the fractional part.
Final Result: Fraction Form of 0.1405 After simplifying, we get the final fraction:
Answer: 0.1405 = 281/2000
Converting 0.1405 to a fraction results in 281/2000. 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.