Place Value

Lesson Objectives

By the end of this lesson, students should be able to:

Understand the concept of place value
Identify and distinguish between digit, place, and value
Apply place value to solve real-world problems

Lesson Introduction

Place value is the value of each digit in a number based on its position. Understanding place value is crucial for reading, writing, and comparing numbers correctly. It forms the foundation of the number system and is essential in every area of mathematics.

Definition of Place Value

Every digit in a number has a place and a value. The place refers to the position the digit holds in the number, and the value is what the digit is worth based on its position.

Digit, Place, and Value

For example, in the number $4,836$ :

Digit: 8
Place: Hundreds
Value: $800$

Place Value in Whole Numbers

Place values increase by a factor of 10 from right to left. Example:

Ones
Tens
Hundreds
Thousands
Ten Thousands
Hundred Thousands

Place Value in Decimals

Decimal places decrease by a factor of 10 from left to right after the decimal point:

Tenths
Hundredths
Thousandths

Expanded Form

Expanded form expresses a number by showing the value of each digit. Example: $3,204 = 3,000 + 200 + 0 + 4$

Examples

Example 1: What is the place value of 7 in 3,728?

$7$ is in the hundreds place. So, the value is $700$ .

Answer: $700$

Example 2: Find the value of 5 in 45,321.

$5$ is in the thousands place. Value = $5,000$

Answer: $5,000$

Example 3: Write 6,304 in expanded form.

$6,304 = 6,000 + 300 + 0 + 4$

Answer: $6,000 + 300 + 0 + 4$

Example 4: Express 50,020 in expanded form.

$50,020 = 50,000 + 0 + 0 + 20 + 0$

Answer: $50,000 + 0 + 0 + 20 + 0$

Example 5: What is the digit in the thousandths place of 4.5289?

Thousandths place = third digit after decimal = $8$

Answer: $8$

Example 6: What is the value of 2 in 9.432?

$2$ is in the thousandths place = $\frac{2}{1000} = 0.002$

Answer: $0.002$

Example 7: Identify the digit in the hundredths place of 3.149.

$4$ is in the hundredths place.

Answer: $4$

Example 8: Find the value of the digit 9 in 0.0391

$9$ is in the thousandths place = $0.009$

Answer: $0.009$

Example 9: Round 7.853 to the nearest hundredth.

Hundredth digit = 5; thousandth = 3 → leave 5 → $7.85$

Answer: $7.85$

Example 10: Round 9.667 to the nearest tenth.

Tenth = 6; hundredth = 6 → round up → $9.7$

Answer: $9.7$

Exercises

What is the value of 6 in 6,482?
[WAEC] What is the digit in the hundredth place of 3.456?
(Past Question)
Write 24,035 in expanded form.
[NECO] Identify the value of 2 in 7.428.
(Past Question)
What is the digit in the tenths place in 5.63?
Find the value of 7 in 70,000.
[JAMB] What is the place value of 3 in 93.05?
(Past Question)
Round 6.789 to the nearest hundredth.
[NABTEB] Express 50,206 in expanded form.
(Past Question)
What is the value of 5 in 0.054?

Conclusion/Recap

Place value is the bedrock of understanding numbers. It helps you interpret, write, and manipulate numbers accurately. Knowing the difference between digit, place, and value allows you to confidently solve problems involving whole numbers and decimals, paving the way for more advanced math concepts.