# What is 6.75 as a fraction?

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**.

- We start with the number
**For the denominator:**- Each position after the decimal represents a division by
**10**. - Thus, having
**2**positions after the decimal equates to**100**or**10**.^{2}

- Each position after the decimal represents a division by
**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):

**$6.75=\frac{6.75}{1}=\frac{\mathrm{6.75\; \times \; 100}}{\mathrm{1\; \times \; 100}}=\frac{675}{100}=\frac{\mathrm{675\xf725}}{\mathrm{100\xf725}}=\frac{27}{4}$**

## 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**= 10**^{2}= 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.**$\frac{\mathrm{6.75\; \times \; 100}}{\mathrm{1\; \times \; 100}}$ = $\frac{675}{100}$****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.**$\frac{\mathrm{675\; \xf7\; 25}}{\mathrm{100\; \xf7\; 25}}$ = $\frac{27}{4}$**

### 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.