What is 2.77 as a fraction?

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 2.77 to a fraction.

You can try other values to get more familiar with the conversion process.

Often, convert 2.76 to a fraction or 2.77777 to a fraction, depending on the task.

Understanding the decimal: “2.77”

A decimal number consists of an integer part and a fractional part, separated by a decimal point. The integer part is on the left, and the fractional part is on the right. For example, in 2.77, 2 is the integer part and 77 is the fractional part.

Conversion Explanation:

  1. For the numerator:
    • We start with the number 2.77.
    • By removing the decimal point, we derive the numerator as 277.
  2. For the denominator:
    • Each position after the decimal represents a division by 10.
    • Thus, having 2 positions after the decimal equates to 100 or 102.
  3. Factors:
    • The factors for the numerator and the denominator are numbers that can evenly divide each of them.
    • For instance, the factors of 277 include 1, and 277.
    • The factors of 100 comprise 1, 2, 4, 5, 10, 20, 25, 50, and 100.
  4. Greatest Common Divisor (GCD):
    • It's the largest number that can evenly divide both the numerator and the denominator.
    • In this instance, the GCD for 277 and 100 is 1.

The factors of 277 are:

1 277

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

2.77=2.771=2.77 × 1001 × 100=277100=277÷1100÷1=277100

Solution:

2.77 = 277100

What is a decimal?

A decimal is a numeral system that includes a point to separate the whole number part from the fractional part. This system makes it easy to work with numbers less than one.

What is a fraction?

A fraction is a mathematical way of showing a part of a whole. It has two parts: the numerator on top and the denominator below, which help express partial values and comparisons.

Step-by-step solution:

  • Step 1: First, write the decimal as a fraction over 1. This sets up the next steps. 2.77 = 2.771
  • Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 2.77, we have three digits. This means multiplying the fraction by a factor of 10 for each digit. Factor = 102 = 100
  • Step 3: Using this factor, multiply both the numerator and the denominator. 2.77 × 1001 × 100 = 277100
  • Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 1. Divide both the numerator and the denominator by this common divisor. 277 ÷ 1100 ÷ 1 = 277100

Answer in mixed fraction format:

2.77 =
2
77
100