Understanding Place Value

How does a digit's position determine its value?

📚

Standard

NBT.1

📅

Grade

5th

⏱️

Duration

60m

📋 Standards & Objectives

📐Standard

5.NBT.1Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

🎯SWBAT

Identify the place value and value of any digit in a whole number
Identify the place value and value of any digit in a decimal
Explain how a digit's value changes by ×10 or ÷10 when it shifts position

🚀 Place Value Is Everywhere!

💰Money Matters

$1,234.56 — Each digit has a different job! The 1 is worth $1,000, the 2 is worth $200, the 3 is worth $30, the 4 is worth $4, and the 5 is worth 50 cents!

👥Population

Spokane has 228,989 people. The first 2 represents 200,000 people, the second 2 represents 20,000 people. Same digit, different position, different value!

🪐Space Science

Earth is 93,000,000 miles from the Sun. We can understand huge numbers by knowing what each digit represents!

📚 Key Vocabulary

🔢Place Value

The position of a digit in a number. Examples: ones, tens, hundreds, thousands, millions.

✏️Digit

The symbols we use to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Each digit can be placed in different positions.

💎Value

What a digit is worth based on its place. The 5 in 500 is worth 500. The 5 in 50 is worth 50.

📦Period

Groups of three digits separated by commas: ones period, thousands period, millions period, billions period.

✨ The Place Value Chart

Let's see where each digit goes in 784,265,319:

Hundred Millions

Ten Millions

Millions

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

7

8

4

2

6

5

3

1

9

✨ Finding a Digit's Value

Use this formula:

Digit × Place Value = Value

Example: In 784,265,319, what is the value of the 5?

1

Find the place value of the 5: Thousands (1,000)

2

Multiply: 5 × 1,000 = 5,000

3

The 5 has a value of 5,000

👨‍🏫 I Do: Finding Value (Whole Numbers)

Level 1: Whole Numbers

Question: In 784,265,319, what is the value of the 5?

784,265,319

1

The 5 is in the Thousands place

2

5 × 1,000 = 5,000

Answer:

5,000

👨‍🏫 I Do: Finding Value

Level 1: Whole Numbers

Question: In 9,372,645, what is the value of the 3?

9,372,645

1

The 3 is in the Hundred Thousands place

2

3 × 100,000 = 300,000

Answer:

300,000

👥 We Do: Finding Value

Level 2: Together

Question: In 284,625,103, what is the value of the 6?

284,625,103

1

The 6 is in the Hundred Thousands place (100,000)

2

6 × 100,000 = 600,000

Answer:

600,000

👥 We Do: Finding Value

Level 2: Together

Question: In 491,528, what is the value of the 4?

491,528

1

The 4 is in the Hundred Thousands place (100,000)

2

4 × 100,000 = 400,000

Answer:

400,000

✏️ You Do: Finding Value

Level 3: Independent

Question: In 3,816,472, what is the value of the 8?

3,816,472

Work this one on your own! Hint: Find the place value first, then multiply.

1

The 8 is in the Hundred Thousands place (100,000)

2

8 × 100,000 = 800,000

Answer:

800,000

✏️ You Do: Finding Value

Level 3: Independent

Question: In 52,937,610, what is the value of the 9?

52,937,610

Work this one on your own! Hint: Find the place value first, then multiply.

1

The 9 is in the Hundred Thousands place (100,000)

2

9 × 100,000 = 900,000

Answer:

900,000

✨ Decimal Place Values

Decimals extend the place value chart to the right of the decimal point:

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

.

Tenths

Hundredths

Thousandths

2

6

5

3

1

9

.

8

4

7

Tenths: 1 ÷ 10 = 0.1

Hundredths: 1 ÷ 100 = 0.01

Thousandths: 1 ÷ 1,000 = 0.001

👨‍🏫 I Do: Finding Value (Decimals)

Level 1: Decimals

Question: In 265,319.847, what is the value of the 4?

265,319.847

1

The 4 is in the Hundredths place (0.01)

2

4 × 0.01 = 0.04

Answer:

0.04

👨‍🏫 I Do: Finding Value

Level 1: Decimals

Question: In 56,912.734, what is the value of the 7?

56,912.734

1

The 7 is in the Tenths place (0.1)

2

7 × 0.1 = 0.7

Answer:

0.7

👥 We Do: Finding Value

Level 2: Together

Question: In 2,485.396, what is the value of the 3?

2,485.396

1

The 3 is in the Tenths place (0.1)

2

3 × 0.1 = 0.3

Answer:

0.3

👥 We Do: Finding Value

Level 2: Together

Question: In 80,622.54, what is the value of the 5?

80,622.54

1

The 5 is in the Tenths place (0.1)

2

5 × 0.1 = 0.5

Answer:

0.5

✏️ You Do: Finding Value

Level 3: Independent

Question: In 63,248.517, what is the value of the 1?

63,248.517

Work this one on your own! Hint: The 1 is in a decimal place.

1

The 1 is in the Hundredths place (0.01)

2

1 × 0.01 = 0.01

Answer:

0.01

✏️ You Do: Finding Value

Level 3: Independent

Question: In 7,450.283, what is the value of the 8?

7,450.283

Work this one on your own! Hint: The 8 is in a decimal place.

1

The 8 is in the Hundredths place (0.01)

2

8 × 0.01 = 0.08

Answer:

0.08

✨ The ×10 / ÷10 Pattern

Look at how digits relate to their neighbors in 522,894.737:

Hundred Thousands

Ten Thousands

Thousands

Hundreds

Tens

Ones

.

Tenths

5

2

8

9

4

.

7

Moving LEFT: Each place is ×10 the place to its right

Example: The 8 (Hundreds = 800) is 10 times the 9 (Tens = 90)

Moving RIGHT: Each place is ÷10 the place to its left

Example: The 7 (Tenths = 0.7) is 1/10 of the 4 (Ones = 4)

👨‍🏫 I Do: Comparing Place Values

Level 1: ×10 / ÷10 Patterns

Question: In 56,442.39, compare the two 4s.

56,442.39

1

First 4: Hundreds place = 400 | Second 4: Tens place = 40

2

400 is 10 times as much as 40 | 40 is 1/10 of 400

Relationship:

400 = 10 × 40

👥 We Do: Comparing Place Values

Level 2: Together

Question: In 23,936.7, compare the two 3s.

23,936.7

1

First 3: Thousands = 3,000 | Second 3: Tens = 30

2

3,000 is 100 times as much as 30 | 30 is 1/100 of 3,000

Relationship:

3,000 = 100 × 30

✏️ You Do: Comparing Place Values

Level 3: Independent

Question: In 84,571.58, compare the two 5s.

84,571.58

Work this one on your own! Hint: One 5 is in the hundreds place, the other is in the tenths place.

1

First 5: Hundreds = 500 | Second 5: Tenths = 0.5

2

500 is 1,000 times 0.5 | 0.5 is 1/1,000 of 500

Relationship:

500 = 1,000 × 0.5

🏆 Challenge Round!

Complete each statement. Click to check!

300 is 10 times as much as ___

30

300 is 1/10 as much as ___

3,000

0.4 is 10 times as much as ___

0.04

0.4 is 1/10 as much as ___

4

💬 Turn & Talk

Discuss with a partner:

Question 1: Why is understanding the ×10 / ÷10 pattern helpful when working with place value?

Question 2: How is the decimal place value system related to the whole number place value system?

📝 Key Takeaways

📊

Place Value Matters

A digit's position in a number determines its actual value. The same digit (like 5) is worth different amounts depending on its place.

✖️➗

The ×10 / ÷10 Pattern

Each place is 10 times the place to its right and 1/10 of the place to its left. This pattern works for whole numbers AND decimals!

🔢

Whole & Decimal Places

The decimal point separates whole number places from decimal places. Tenths = 0.1, Hundredths = 0.01, Thousandths = 0.001.

🌍

Real-World Connection

From money to population to science, place value helps us understand and communicate about large numbers and small decimal amounts.

🎫 Exit Ticket

Answer these questions to show what you've learned!

1. In 47,056,918.32, what is the value of the 5?

50,000

The 5 is in the Ten Thousands place: 5 × 10,000 = 50,000

2. In 8,425.363, what is the value of the 3 in the hundredths place?

0.03

The 3 is in the Hundredths place: 3 × 0.01 = 0.03

3. The 4 in 65,742.183 = 40. The 4 in 94.506 = 4. 40 is ___ times the value of 4.

10 times

40 ÷ 4 = 10, so 40 is 10 times as much as 4