What is 0.1405 as a fraction in simplest form.

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 Decimal

The 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 Fraction

Focus on converting the decimal part, 0.1405, to a fraction. To do this, consider the place value of the decimal:

0.1405 =

1405

10000


Step 3: Simplify the Fraction

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 Fraction

Now 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



Conclusion

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.

Calculated Values List