Answer: 0.2775 as a fraction is 111/400
Converting the decimal number 0.2775 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 0.2775 can be broken down as:
0.2775 = 0 + 0.2775
Here, 0 is the whole number part, and 0.2775 is the decimal part.
Step 2: Convert the Decimal to a FractionFocus on converting the decimal part, 0.2775, to a fraction. To do this, consider the place value of the decimal:
0.2775 =
2775
10000
Now, simplify the fraction 2775/10000. To do this, find the greatest common divisor (GCD) of 2775 and 10000.
Now, divide both the numerator and the denominator by their GCD:
2775 ÷ 25
10000 ÷ 25
=
111
400
So, 0.2775 as a fraction is 111/400
Step 4: Combine the Whole Number and FractionNow that you have 0.2775 = 0 + 0.2775, express the entire number as a mixed fraction:
0.2775
= 0 +
111
400
=
0
400
+
111
400
=
111
400
Here, 0/400 is the whole number 0, and 111/400 is the fractional part.
Final Result: Fraction Form of 0.2775 After simplifying, we get the final fraction:
Answer: 0.2775 = 111/400
Converting 0.2775 to a fraction results in 111/400. 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.