# 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 example, in 0.75, the number represents three-quarters.

## What is a fraction?

A fraction shows 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 combines a whole number and a fraction. It shows a quantity more than one but not a round number. For example, 3 1/2 means three and a half.

## What is a percentage?

A percentage expresses a number as a fraction of 100. It's denoted by the "%" symbol. So, 50% means fifty out of every hundred.

## Converting Fractions to Percentages

Learn four simple ways to convert fractions into percentages.

### Scaling Method

**Basics:**

A fraction shows a part of a whole. The numerator is the part we are looking at, and the denominator is the total parts. Percentages represent parts out of 100.

**Conversion Process:**

To convert a fraction to a percentage, make the denominator 100. Here's how:

- Find the factor to scale the denominator to
**100**. - Multiply both the numerator and the denominator by this factor.
- The new fraction will have a denominator of
**100**, making the numerator the 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%**.

### Decimal Conversion

**Basics:**

You can convert any fraction to a decimal by dividing the numerator by the denominator. Once it's a decimal, turning it into a percentage is simple.

**Conversion Process:**

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

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

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

## Converting Mixed Fractions to Percentages

Let's see how to convert mixed fractions to percentages.

**Understanding Mixed Fractions**

A mixed fraction has both a whole number and a fraction. For example, in 2 3/4, '2' is the whole number and '3/4' is the fraction.

### Converting a Mixed Fraction to an Improper Fraction

**Step-by-Step Process:**

- Multiply the whole number by the fraction's denominator.
- Add the numerator to this product.
- Use this sum as the new numerator, keeping the same 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**

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

**Example:**

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

## Converting Decimals to Percentages

Knowing how to convert decimals to percentages is useful in both school and everyday life.

Decimals: A decimal shows part of a whole number. It is based on powers of ten and is indicated by a decimal point.

Any decimal can be shown as a fraction of 100, which is a percentage.

### Conversion Process

- Take the given decimal number;
- Multiply it by
**100**; - Add the
**%**symbol to your result.

This shifts the decimal point two places to the right, making the decimal a whole number, which is then shown as a fraction of 100.

**Example:**

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

**Interpreting the Result**

When converting 0.45 to 45%, it means that 0.45 is 45% of the whole, or 45 parts out of 100. This makes it easier to visualize and compare to other values.

## Converting Whole Numbers to Percentages

This is the simplest conversion process.

Whole Numbers: These are positive integers, including zero, without fractions or decimals.

### Basic Conversion Method

Converting whole numbers to percentages is straightforward. It’s about comparing the number to 100.

**Conversion Process:**

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

**Example:**

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

**3 × 100 = 300%**

**Understanding the Result**

By converting 3 to 300%, you're saying that 3 is 300% of 1. This means 1 is 100%, so 3 times that amount is 300%.

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

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

Divide 3/5 to get a decimal, then multiply to get the percent.

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

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

Divide 4/5 to get a decimal, then multiply for the percent.

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

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

Divide 1/8 to get a decimal, then multiply to get the percent.

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

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

Convert 2/3 to decimal by dividing, then multiply to get percent.

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

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

Get the percent of 5/8 by dividing and then multiplying.

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

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

Convert 1/3 to percent by dividing and then multiplying.

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

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

Convert 17/20 to decimal by dividing, then find its percent.

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

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

To express 2/5 as a percent, divide and then multiply by 100.

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

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

Divide 3/4 to get a decimal, then multiply by 100 for the percent.

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

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

To get the percent of 3/8, divide and then multiply by 100.

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

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

Divide 1/4 to get a decimal, then multiply by 100 for the percent.

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

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

Divide 1/5 to get a decimal, then multiply to find the percent.