Answer: 0.2776 as a fraction is 347/1250
Converting the decimal number 0.2776 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 0.2776 can be broken down as:
0.2776 = 0 + 0.2776
Here, 0 is the whole number part, and 0.2776 is the decimal part.
Step 2: Convert the Decimal to a FractionFocus on converting the decimal part, 0.2776, to a fraction. To do this, consider the place value of the decimal:
0.2776 =
2776
10000
Now, simplify the fraction 2776/10000. To do this, find the greatest common divisor (GCD) of 2776 and 10000.
Now, divide both the numerator and the denominator by their GCD:
2776 ÷ 8
10000 ÷ 8
=
347
1250
So, 0.2776 as a fraction is 347/1250
Step 4: Combine the Whole Number and FractionNow that you have 0.2776 = 0 + 0.2776, express the entire number as a mixed fraction:
0.2776
= 0 +
347
1250
=
0
1250
+
347
1250
=
347
1250
Here, 0/1250 is the whole number 0, and 347/1250 is the fractional part.
Final Result: Fraction Form of 0.2776 After simplifying, we get the final fraction:
Answer: 0.2776 = 347/1250
Converting 0.2776 to a fraction results in 347/1250. 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.