What is 0.7742 as a fraction in simplest form.

Converting the decimal number 0.7742 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 0.7742 Decimal as a Fraction

Step 1: Understand the Decimal

The decimal 0.7742 can be broken down as:

Here, 0 is the whole number part, and 0.7742 is the decimal part.

Step 2: Convert the Decimal to a Fraction

Focus on converting the decimal part, 0.7742, to a fraction. To do this, consider the place value of the decimal:

Step 3: Simplify the Fraction

Now, simplify the fraction 7742/10000. To do this, find the greatest common divisor (GCD) of 7742 and 10000.

• The GCD of 7742 and 10000 is 2.

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

So, 0.7742 as a fraction is 3871/5000

Step 4: Combine the Whole Number and Fraction

Now that you have 0.7742 = 0 + 0.7742, express the entire number as a mixed fraction:

Here, 0/5000 is the whole number 0, and 3871/5000 is the fractional part.

Final Result Answer

Fraction Form of 0.7742 After simplifying, we get the final fraction:

Conclusion

Converting 0.7742 to a fraction results in 3871/5000. 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.