# Converting to Percentages

## What is a decimal?

A decimal is a system of numbers based on ten. It uses a point, called a decimal point, to separate the whole number from parts less than one. For instance, in 0.75, the number represents three-quarters.

## What is a fraction?

A fraction depicts how many parts of a certain size there are. It consists of a numerator (above the line) and a denominator (below the line). For example, in 2/3, it means two out of three equal parts.

## What is a mixed fraction?

A mixed fraction is a blend of a whole number and a fraction. It demonstrates a quantity more than one but not a round number. Like 3 1/2, it indicates three and a half.

## What is a percentage?

A percentage is a method of expressing a number as a fraction of 100. It's denoted by the "%" symbol. So, when we say 50%, we mean fifty out of every hundred.

## Converting Fractions to Percentages

Understanding the relationship between fractions and percentages can significantly enhance one's numeracy skills. Now we'll explore three distinct methods to convert fractions into percentages.

### Method of Scaling

**Understanding the Basics:**

A fraction represents a part of a whole. The numerator indicates the part we're examining, the denominator displays the total parts. Percentages, on the other hand, signify parts out of 100.

**Transformation Process:**

To turn a fraction into a percentage, we aim to have a denominator of 100. Here's how:

- Determine the factor to scale the denominator to
**100**. - Multiply both the numerator and the denominator by this factor.
- The resultant fraction will have a denominator of
**100**, making the numerator the desired percentage.

**Example: Convert 3/8 to a percentage**

- Scaling factor
**= $\frac{100}{8}\mathrm{=\; 12.5}$**; - New fraction:
**$\frac{\mathrm{3\; \times \; 12.5}}{\mathrm{8\; \times \; 12.5}}\mathrm{=}\frac{37.5}{100}$**; - Percentage:
**37.5%**.

### Using Decimal Conversion

**Understanding the Basics:**

Every fraction can be translated to a decimal by dividing its numerator by its denominator. Once in decimal form, conversion to percentage becomes straightforward.

**Transformation Process:**

- Divide the numerator by the denominator to get a decimal;
- Multiply the decimal by
**100**to achieve the percentage.

**Example: Convert 3/8 as a percentage**

- Decimal form:
**3 ÷ 8 = 0.375**; - Percentage:
**0.375 × 100 = 37.5%**.

## Converting Mixed Fractions to Percentages

Navigating in the mathematics can sometimes difficult. But if you figure it out, everything becomes simple. We will now look at the process of converting mixed fractions to percentages.

**Understanding Mixed Fractions**

Before diving into conversions, it's crucial to grasp what a mixed fraction is. A mixed fraction contains both a whole number and a proper fraction. For instance, in the mixed fraction 2 3/4, '2' is the whole number, and '3/4' is the fraction.

### Converting the Mixed Fraction to an Improper Fraction

**Step-by-Step Process:**

- Multiply the whole number by the denominator of the fraction.
- Add the numerator of the fraction to this product.
- Use this sum as the new numerator, keeping the original denominator.

**Example:**

Convert **2 3/4** to an improper fraction.

**(2 × 4) + 3 = 11**

Result: **11/4**

**Converting the Improper Fraction to a Decimal**

Divide the numerator by the denominator.

**Example:**

For **11/4, 11 ÷ 4 = 2.75**.

**Converting the Decimal to a Percentage**

After obtaining the decimal, this final step is relatively straightforward.

- Multiply the decimal by
**100**; - Attach the
**%**symbol to your result.

**Example:**

For **2.75** as a decimal, **2.75 × 100 = 275%**.

## Converting Decimals to Percentages

It's important to know how to convert decimals to percentages, both in academy and in real life. This transformation is simple once you grasp the underlying principles. Dive into this to understand the conversion process from decimals to percentages.

Decimals: A decimal represents a part of a whole number. It's based on the power of tens and is denoted using a point known as the decimal point.

Every decimal, when expressed in relation to a whole (i.e., 1), can also be represented as a fraction of 100 – and this fraction is a percentage.

### Conversion Process

- Take the given decimal number;
- Multiply it by
**100**; - Attach the percentage
**(%)**symbol to your result.

This process essentially shifts the decimal point two places to the right. And making decimal to a whole number or “an integer” with a decimal. And then representing that number as a fraction of 100.

**Example:**

Convert the decimal **0.45** into a percentage. **0.45 × 100 = 45%**

**Interpreting the Result**

On converting 0.45 to 45%, we imply that 0.45 is 45% of the entire, or 45 parts out of a total 100. It offers a more relatable way to visualize the value, especially when comparing it to other quantities or values.

## Convert Whole Numbers into Percentages

In the vast universe of mathematics, percentages have in integral role in everyday life. But how do you transition from a simple whole number to a percentage? This guide breaks down this transformation process into easily digestible steps.

Entire Numbers: These are the set of all positive integers, including zero. Essentially, they're numbers without any fractions or decimals.

### Basic Method of Conversion

The essence of converting integers to percentages is simple. Representing a number 'as a percentage' is fundamentally about comparing it to 100.

**Conversion Process:**

- Take the whole number;
- Multiply it by
**100**; - Append the
**%**symbol to the result.

**Example:**

Convert the whole number **'3'** into a percentage.

**3 × 100 = 300%**

**Understanding the Result**

By converting the whole number 3 into 300%, you're essentially saying that 3 is 300% of 1. This might feel counterintuitive at first, but it's accurate in mathematical terms. Essentially, the number 1 is 100%, so 3 times that amount becomes 300%.

**$\frac{3}{5}$**

**What is 3/5 as a percent?**

Seeking 3/5 in percent form? Start with division, and the path clears.

**$\frac{4}{5}$**

**What is 4/5 as a percent?**

Divide to transform 4/5 to decimal; multiply to express in percent.

**$\frac{1}{8}$**

**What is 1/8 as a percent?**

The transformation of 1/8 to percent entails division and multiplication.

**$\frac{2}{3}$**

**What is 2/3 as a percent?**

The fraction 2/3 beckons to its percent side. Answer with division.

**$\frac{5}{8}$**

**What is 5/8 as a percent?**

Decipher the percent realm of 5/8. Let division be your guide.

**$\frac{1}{3}$**

**What is 1/3 as a percent?**

The journey of 1/3 to percent is intriguing. Begin with division.

**$\frac{17}{20}$**

**What is 17/20 as a percent?**

Finding percent for 17/20? Divide first, then multiply the result by 100.

**$\frac{2}{5}$**

**What is 2/5 as a percent?**

In the fraction 2/5, lies a percent secret. Unfold it with division.

**$\frac{3}{4}$**

**What is 3/4 as a percent?**

The fraction 3/4 yields a percent when divided and multiplied by 100.

**$\frac{3}{8}$**

**What is 3/8 as a percent?**

To mathematically infer 3/8 in percent, employ division followed by multiplication.

**$\frac{1}{4}$**

**What is 1/4 as a percent?**

For 1/4, division provides the decimal. Multiplication gives the percent.

**$\frac{1}{5}$**

**What is 1/5 as a percent?**

For a fraction's 1/5, a division produces the decimal. Multiply for percent.

**$\frac{18}{20}$**

**What is 18/20 as a percent?**

Expressing 18/20 in percent involves an initial division and final multiplication.

**$\frac{7}{8}$**

**What is 7/8 as a percent?**

Utilizing division for 7/8 yields a decimal. Multiplication produces percent.

**$\frac{1}{6}$**

**What is 1/6 as a percent?**

The percent essence of 1/6? Dive into division, and it'll emerge.

**$0.4$**

**What is 0.4 as a percent?**

The decimal 0.4 can be expressed in percent by multiplying by 100.

**$\frac{14}{20}$**

**What is 14/20 as a percent?**

Mathematically, 14/20 in percent is a product of division and multiplication.

**$\frac{5}{6}$**

**What is 5/6 as a percent?**

Division elucidates the decimal of 5/6. Multiplication reveals its percent.

**$\frac{7}{10}$**

**What is 7/10 as a percent?**

7/10 has a percent counterpart. Let division unveil its value.

**$\frac{20}{25}$**

**What is 20/25 as a percent?**

Determine the percent of 20/25 by applying division and then multiplication.

**$0.2$**

**What is 0.2 as a percent?**

Decoding decimal 0.2 in percent? Multiply, and the answer is at hand.

**$\frac{1}{2}$**

**What is 1/2 as a percent?**

Using division, the fraction 1/2 can be expressed in percent.

**$\frac{13}{20}$**

**What is 13/20 as a percent?**

Dive deep into 13/20's percent essence. It's just a division beneath.

**$\frac{4}{6}$**

**What is 4/6 as a percent?**

Engage with 4/6's percent side. Just a division away from discovery.