What is 0.8660 as a fraction in simplest form.

Converting the decimal number 0.8660 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 0.8660 Decimal as a Fraction

Step 1: Understand the Decimal

The decimal 0.8660 can be broken down as:

Here, 0 is the whole number part, and 0.866 is the decimal part.

Step 2: Convert the Decimal to a Fraction

Focus on converting the decimal part, 0.866, to a fraction. To do this, consider the place value of the decimal:

Step 3: Simplify the Fraction

Now, simplify the fraction 866/1000. To do this, find the greatest common divisor (GCD) of 866 and 1000.

• The GCD of 866 and 1000 is 2.

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

So, 0.866 as a fraction is 433/500

Step 4: Combine the Whole Number and Fraction

Now that you have 0.8660 = 0 + 0.866, express the entire number as a mixed fraction:

Here, 0/500 is the whole number 0, and 433/500 is the fractional part.

Final Result Answer

Fraction Form of 0.8660 After simplifying, we get the final fraction:

Conclusion

Converting 0.8660 to a fraction results in 433/500. 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.