What is 6.75 as a fraction? Tutorial in mathway.pro

Converting decimals to fractions is an essential skill. It bridges the gap between two numeric representations. In this guide, we will detail the process of converting 6.75 to a fraction.

You can select other values to familiarize yourself with the conversion guide.

Often, convert 6.72 to a fraction or 6.8 to a fraction, depending on the task.

Understanding the decimal: “6.75”

A decimal number has an integer and fractional parts. The decimal point separates the two. The integer is to the left, the fraction to the right. For example, in 6.75, 6 is the integer and 75 is the fraction.

Conversion Explanation:

For the numerator:
- We start with the number 6.75.
- By removing the decimal point, we derive the numerator as 675.
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 675 include 1, 3, 5, 9, 15, 25, 27, 45, 75, 135, 225, and 675.
- 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 675 and 100 is 25.

The factors of 675 are:

1 3 5 9 15 25 27 45 75 135 225 675

The factors of 100 are:

1 2 4 5 10 20 25 50 100

Conversion formula (equation):

$6.75 = \frac{6.75}{1} = \frac{6.75 × 100}{1 × 100} = \frac{675}{100} = \frac{675÷25}{100÷25} = \frac{27}{4}$

Solution:

6.75 = $\frac{27}{4}$

What is a decimal?

A decimal is a numeral system with a point. This point divides the integer from its fractional part. It provides a straightforward way to express and work with values less than one.

What is a fraction?

A fraction is a mathematical expression of two parts: the numerator on top and the denominator below. It represents partial values, showcasing relationships or comparisons.

A fast guide to the conversion:

Numbers exist in different formats: decimals, fractions, and percentages. Today, we'll convert the decimal 6.75 into its fractional form. This conversion shows the core essence of the number. And making mathematical operations more intuitive.

Step-by-step solution:

Step 1: Laying the groundwork. Before diving into conversion, let's frame our decimal as a fraction over 1. This offers a clean slate, making the subsequent steps systematic. 6.75 = $\frac{6.75}{1}$
Step 2: Gauging the decimal's depth. Decimals vary. Some are short; others are long. Our focus? The number of digits after the decimal point. For 6.75, we have three digits. This insight nudges us to elevate our fraction by a factor of 10 for each digit. Factor = 10² = 100
Step 3: Amplifying the fraction. Taking our coefficient, it's time to strengthen both the numerator and denominator. The intent? To equalize the fraction by the depth of the decimal. $\frac{6.75 × 100}{1 × 100}$ = $\frac{675}{100}$
Step 4: Simplifying. Elegance lies in simplicity. Our mission now is to shorten the $\frac{675}{100}$ . This requires seeking common divisors. Here, 25 is our ally, dividing both parts seamlessly. $\frac{675 ÷ 25}{100 ÷ 25}$ = $\frac{27}{4}$

Conclusion:

The decimal 6.75, when unfurled and explored, translates seamlessly into the fraction 6.75/1. This manual provides an introduction to numbers and deepens number skills. Such conversions, though seemingly elementary, pave the way for advanced mathematical prowess.

Answer in mixed fraction format:

6.75 =

6

3

4

What is 6.75 as a fraction?