What is 0.7850 as a fraction in simplest form.

Converting the decimal number 0.7850 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.

How to write 0.7850 Decimal as a Fraction

Step 1: Understand the Decimal

The decimal 0.7850 can be broken down as:

Here, 0 is the whole number part, and 0.785 is the decimal part.

Step 2: Convert the Decimal to a Fraction

Focus on converting the decimal part, 0.785, to a fraction. To do this, consider the place value of the decimal:

Step 3: Simplify the Fraction

Now, simplify the fraction 785/1000. To do this, find the greatest common divisor (GCD) of 785 and 1000.

• The GCD of 785 and 1000 is 5.

Now, divide both the numerator and the denominator by their GCD:

So, 0.785 as a fraction is 157/200

Step 4: Combine the Whole Number and Fraction

Now that you have 0.7850 = 0 + 0.785, express the entire number as a mixed fraction:

Here, 0/200 is the whole number 0, and 157/200 is the fractional part.

Final Result Answer

Fraction Form of 0.7850 After simplifying, we get the final fraction:

Conclusion

Converting 0.7850 to a fraction results in 157/200. 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.