What is 3.12 as a fraction? Tutorial in mathshowcase.info

Converting decimals to fractions can be useful in many situations. Let's go through the steps to convert a decimal 3.12 to a fraction.

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

Often, convert 3.1 to a fraction or 3.125 to a fraction, depending on the task.

Understanding the decimal: “3.12”

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 3.12, 3 is the integer part and 12 is the fractional part.

Conversion Explanation:

For the numerator:
- We start with the number 3.12.
- By removing the decimal point, we derive the numerator as 312.
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.
Factors:
- The factors for the numerator and the denominator are numbers that can evenly divide each of them.
- For instance, the factors of 312 include 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, and 312.
- The factors of 100 comprise 1, 2, 4, 5, 10, 20, 25, 50, and 100.
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 312 and 100 is 4.

The factors of 312 are:

1 2 3 4 6 8 12 13 24 26 39 52 78 104 156 312

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

$3.12 = \frac{3.12}{1} = \frac{3.12 × 100}{1 × 100} = \frac{312}{100} = \frac{312÷4}{100÷4} = \frac{78}{25}$

Solution:

3.12 = $\frac{78}{25}$

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. 3.12 = $\frac{3.12}{1}$
Step 2: Decimals can have different lengths. We will align the number of digits after the decimal point. For 3.12, 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. $\frac{3.12 × 100}{1 × 100}$ = $\frac{312}{100}$
Step 4: Now we need to simplify the fraction by finding common divisors. The greatest common divisor is 4. Divide both the numerator and the denominator by this common divisor. $\frac{312 ÷ 4}{100 ÷ 4}$ = $\frac{78}{25}$

Answer in mixed fraction format:

3.12 =

3

25

What is 3.12 as a fraction?