Decimal Lesson: Understanding Decimals and Their Operations

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Updated: Apr 15, 2025

Lesson

Decimals are a crucial part of mathematics and are used to represent parts of a whole in a more precise way. Unlike fractions, which represent parts of a whole as a ratio, decimals use the base-10 number system and are written with a decimal point to separate the whole number part from the fractional part.

In this lesson, we will explore the basics of decimals, including how to read, write, compare, and perform operations like addition, subtraction, multiplication, and division with decimals.

What Are Decimals?

A decimal is a number that has a whole part and a fractional part, separated by a decimal point. The decimal system is based on powers of 10, with each place value representing a fraction of 10.

Decimal Places:

Tenths: The first place to the right of the decimal point represents 1/10 of the whole number.
Hundredths: The second place to the right represents 1/100 of the whole number.
Thousandths: The third place represents 1/1000 of the whole number.

For example, 3.75 means 3 whole and 75 hundredths. It is the same as 3 75/100.

Reading and Writing Decimals

Reading and writing decimals is straightforward once you understand the place value system. Let's go over how to read and write decimals:

Example 1: Reading 0.5

The 5 is in the tenths place, so this is read as five tenths or 0.5.

Example 2: Reading 1.25

The 1 is the whole part, and the 25 is in the hundredths place, so this is read as one and twenty-five hundredths or 1.25.

Writing Decimals:

To write a decimal, use a decimal point to separate the whole number from the fractional part. For example, two and three tenths is written as 2.3.

Comparing Decimals

To compare decimals, look at each place value from left to right. Start with the whole number part and move to the right. If the whole number part is the same, compare the digits in the decimal places.

Example 1:

0.6 is greater than 0.5 because the 6 tenths is greater than the 5 tenths.

Example 2:

1.75 is less than 1.8 because 75 hundredths is less than 80 hundredths.

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Decimal Place Value Quiz Exam!

Rounding Decimals

Rounding decimals involves adjusting the number to the nearest value at a specified place value, such as rounding to the nearest tenth, hundredth, or whole number. Here are the rounding rules:

Rounding Rules:

If the digit to the right is 5 or greater, round up.
If the digit to the right is less than 5, round down.

Example 1: Rounding 3.67 to the nearest tenth

The digit in the hundredths place is 7, which is greater than 5, so we round up to 3.7.

Example 2: Rounding 5.23 to the nearest whole number

The digit in the tenths place is 2, which is less than 5, so we round down to 5.

Adding and Subtracting Decimals

When adding or subtracting decimals, it's essential to align the decimal points and then perform the operation as you would with whole numbers.

Example 1: Adding Decimals

Add 2.35 and 1.4:

Line up the decimal points:

2.35

1.40

3.75

The sum is 3.75.

Example 2: Subtracting Decimals

Subtract 5.7 from 9.8:

Line up the decimal points:

9.80

5.70

4.10

The difference is 4.10.

Multiplying and Dividing Decimals

Multiplying and dividing decimals follows the same basic principles as multiplying and dividing whole numbers, but with attention to the decimal point.

Example 1: Multiplying Decimals

Multiply 0.6 by 0.2:

Multiply as if the decimals weren't there: 6 × 2 = 12.
Then count the total number of decimal places. There are two decimal places in total (one in each number), so place the decimal point two places from the right: 0.6 × 0.2 = 0.12.

Example 2: Dividing Decimals

Divide 12.6 by 3:

Divide as if the decimals weren't there: 12.6 ÷ 3 = 4.2.
Since there's only one decimal place in 12.6, place the decimal point in the quotient.

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