Place Value and Decimal Lesson: Understanding the Basics

In mathematics, place value and decimals are fundamental concepts that help us understand and work with numbers. Place value refers to the value of each digit in a number based on its position, while decimals are used to represent numbers that are less than a whole.

Understanding these concepts is essential for reading, writing, and comparing numbers in everyday life. In this lesson, we will explore the place value system, how to read and write decimal numbers, and how to compare numbers using place value and decimals.

What is Place Value?

Place value refers to the value of a digit depending on its position within a number. In our base-10 system (decimal system), each place represents a power of 10.

The value of a number changes depending on where its digits are placed-whether they are in the ones place, tens place, hundreds place, or further to the right, in places like tenths, hundredths, and thousandths.

Understanding Place Value Chart:

Consider the number 4,526:

• 4 is in the thousands place, so it represents 4,000.
• 5 is in the hundreds place, so it represents 500.
• 2 is in the tens place, so it represents 20.
• 6 is in the ones place, so it represents 6.

Thus, 4,526 can be expanded as: 4,000+500+20+6=4,526

Expanded Form:

The expanded form of a number is a way of showing the number as the sum of its place values.

For example: 4,526=4×1,000+5×100+2×10+6×1

This helps you see how the value of each digit is determined by its position.

What Are Decimals?

Decimals are a way of representing numbers that are less than one. In the decimal system, the digits to the right of the decimal point represent parts of a whole. The first digit to the right represents tenths, the second represents hundredths, and the third represents thousandths, and so on.

Decimal Places:

• Tenths: The first digit after the decimal point represents 1/10 (one tenth).
• Hundredths: The second digit represents 1/100 (one hundredth).
• Thousandths: The third digit represents 1/1,000 (one thousandth).

For example, 3.75 means 3 whole and 75 hundredths.

Reading and Writing Decimals

In decimals, the number to the left of the decimal point represents the whole part, while the number to the right represents the fractional part.

Example 1:

The decimal 0.5 represents 5 tenths or 5/10. It is the same as the fraction 1/2.

Example 2:

The decimal 1.25 represents 1 whole and 25 hundredths or 25/100. It is the same as the fraction 1 25/100, which can be simplified to 1 1/4.

Example 3:

The decimal 0.75 represents 75 hundredths or 75/100. It is the same as the fraction 3/4.

Comparing Decimals

To compare decimals, you need to look at the digits from left to right, starting with the whole number part. If the whole number part is the same, compare the digits after the decimal point.

Example:

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

Example:

1.25 is less than 1.5 because the whole number part (1) is the same, but 25 hundredths is less than 50 hundredths.

Rounding Decimals

Rounding decimals involves adjusting a decimal to the nearest whole number, tenth, hundredth, etc., based on specific rules.

Rounding Rules:

1. If the digit to the right of the decimal place is 5 or greater, round up.
2. If the digit to the right is less than 5, round down.

Example:

Rounding 4.67 to the nearest tenth:

• The digit in the hundredths place is 7, which is greater than 5, so we round up to 4.7.

Example:

Rounding 3.24 to the nearest whole number:

• The digit in the tenths place is 2, which is less than 5, so we round down to 3.

Take This Quiz:

Decimal Place Value Quiz Exam!

Adding and Subtracting Decimals

When adding or subtracting decimals, it's important to align the decimal points.

Example 1: Adding Decimals

Add 2.5 and 3.75:

• Align the decimal points: Copy2.50
• 3.75 6.25 Copy
• The sum is 6.25.

Example 2: Subtracting Decimals

Subtract 4.8 from 7.3:

• Align the decimal points: Copy7.30
• 4.80 2.50 Copy
• The difference is 2.50.

Multiplying and Dividing Decimals

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

Example 1: Multiplying Decimals

Multiply 0.6 by 0.3:

• Multiply as if the decimals weren't there: 6 × 3 = 18.
• Then count the total number of decimal places in both numbers. There are two decimal places in total (one in each number), so place the decimal point two places from the right: 0.6 × 0.3 = 0.18.

Example 2: Dividing Decimals

Divide 1.2 by 0.4:

• Divide as if the decimals weren't there: 12 ÷ 4 = 3.
• Now, place the decimal point: 1.2 ÷ 0.4 = 3.

Take This Quiz:

How Well Do You Know Place Value and Decimal?

Practice Problems for Place Value and Decimals

Let's test your understanding of place value and decimals with these practice problems:

1. What is 5.67 rounded to the nearest whole number?
2. Add 4.5 and 2.35.
3. Subtract 8.9 from 12.7.
4. Multiply 0.4 by 0.5.
5. Divide 6.4 by 0.8.