Decimals101

Decimals are everywhere in life – from prices at the store to measurements in recipes. They are a way to express parts of a whole, just like fractions, but they’re often easier to understand because they use a point (the decimal point) to separate whole numbers from fractional parts. In this lesson, we’ll explore how to add, subtract, multiply, and divide decimals.

Contents

• Introduction
• What Are Decimals?
• How to Read Decimals
• How to Add and Subtract Decimals
  • Step-by-Step Addition of Decimals
  • Step-by-Step Subtraction of Decimals
• How to Multiply and Divide Decimals
  • Step-by-Step Multiplication of Decimals
  • Step-by-Step Division of Decimals
• YouTube Video: Basics of Decimals
• Practice Questions
• Key Takeaways

Introduction

Have you ever seen a price tag that reads $3.99? That’s an example of a decimal. Decimals allow us to represent parts of a whole number in a more precise way. In this lesson, we’ll learn how to work with decimals – from addition and subtraction to multiplication and division.

What Are Decimals?

A decimal is a way of writing fractions in a base-10 system. For example, represents half of a whole, or .

A decimal has two parts:

1. The whole number part – the digits before the decimal point.
2. The fractional part – the digits after the decimal point.

Example:

• is read as “three and twenty-five hundredths.”
  • 3 is the whole number part.
  • 25 is the fractional part, representing .

How to Read Decimals

Reading decimals is similar to reading whole numbers, except you say “point” for the decimal separator. The digits after the decimal point represent tenths, hundredths, thousandths, etc.

For example:

• is read as “zero point seven.”
• is read as “twelve point three four five.”

Reminder: The position of the digits after the decimal point determines its value:

• The first digit after the decimal is in the tenths place.
• The second digit is in the hundredths place.
• The third digit is in the thousandths place, and so on.

How to Add and Subtract Decimals

Adding and subtracting decimals is very similar to whole numbers, but we need to line up the decimal points to ensure we’re adding or subtracting the correct place values.

Step-by-Step Addition of Decimals

Example 1:

Add and .

Step 1: Align the decimal points.

Step 2: Add the digits from right to left, just like regular addition.

• (write down 2 and carry over 1)

Step 3: Place the decimal point in the result.

The answer is .

Result:

Step-by-Step Subtraction of Decimals

Example 2:

Subtract from .

Step 1: Align the decimal points.

Step 2: Subtract the digits from right to left.

• (borrow from the 9) =

Step 3: Place the decimal point in the result.

The answer is .

Result:

How to Multiply and Divide Decimals

Step-by-Step Multiplication of Decimals

Multiplying decimals is similar to multiplying whole numbers, but we need to count how many decimal places are in the numbers we’re multiplying.

Example 3:

Multiply by .

Step 1: Ignore the decimal points temporarily and multiply the numbers like whole numbers.

Step 2: Count the total number of decimal places in the original numbers.

• has 1 decimal place.
• has 1 decimal place.

So, there are a total of 2 decimal places.

Step 3: Place the decimal point in the result.

Move the decimal point 2 places to the left.

Result:

Step-by-Step Division of Decimals

Dividing decimals is similar to dividing whole numbers, but you need to adjust the decimal point in the divisor and the dividend so that the divisor becomes a whole number.

Example 4:

Divide by .

Step 1: Move the decimal points in both the dividend and divisor so the divisor becomes a whole number.

• becomes .
• becomes .

Step 2: Divide as you would with whole numbers.

Step 3: Place the decimal point in the result.

Since we moved the decimal 1 place in both numbers, there’s no need to move the decimal point in the result.

Result:

YouTube Video: Basics of Decimals

Watch this video to get a more visual and detailed explanation of decimals, including how to add, subtract, multiply, and divide them with step-by-step examples.

Practice Questions

Key Takeaways

• Decimals are used to represent parts of a whole, separated by a decimal point.
• Always align the decimal points when adding or subtracting decimals.
• When multiplying or dividing decimals, count the total decimal places and adjust the result accordingly.

Keep practicing with decimals to improve your skills!