Place Value Comparisons
Understanding ×10 and ÷10 Relationships
The Big Picture 🗺️
Let's see all the place values from millions to thousandths!
📊 The Complete Place Value Chart
| MILLIONS | THOUSANDS | ONES | . | DECIMALS | ||||||||
| Hundred Millions | Ten Millions | Millions | Hundred Thousands | Ten Thousands | Thousands | Hundreds | Tens | Ones | Tenths | Hundredths | Thousandths | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 7 | 8 | 4 | 2 | 6 | 5 | 3 | 1 | 9 | 8 | 4 | 7 | |
As you move LEFT, each place is 10 times bigger.
As you move RIGHT, each place is 10 times smaller (or ÷10).
🎯 Place vs. Value
Every digit has TWO things: its PLACE and its VALUE
PLACE
Tens
Where is the digit?
VALUE
20
What is it worth? (2 × 10)
What's the difference between saying "the 2 is in the tens place" vs "the 2 has a value of 20"?
Finding the Value 💰
Practice writing the VALUE of underlined digits
✏️ What is the VALUE of the underlined digit?
Step 1: Find the PLACE → The 1 is in the tens place
Step 2: Calculate the VALUE → 1 × 10 = 10
Value = 10
✏️ What is the VALUE of the underlined digit?
1. What PLACE is the 9 in?
2. What is 9 × that place value?
The 9 is in the hundredths place
9 × 0.01 = 0.09
⚡ Quick Practice: Find the Value!
A. 9,372,645
2,000
B. 80,622.54
2
C. 4,915.3
0.3
D. 567,249.380
0 (zero thousandths)
The ×10 Pattern 🔟
Understanding "10 times" and "1/10" relationships
🔟 Moving LEFT = ×10
Each place to the LEFT is 10 times the place to its right!
30 is 10 times the value of 3
300 is 10 times the value of 30
3,000 is 10 times the value of 300
➗ Moving RIGHT = ÷10 (or 1/10)
Each place to the RIGHT is 1/10 (one tenth) of the place to its left!
500 is 1/10 the value of 5,000
50 is 1/10 the value of 500
5 is 1/10 the value of 50
🔢 The Pattern Continues with Decimals!
0.7 is 1/10 the value of 7
0.07 is 1/10 the value of 0.7
7 is 10 times the value of 0.7
0.7 is 10 times the value of 0.07
✏️ Complete the Statements
Same Digit, ONE Number 🔍
Comparing the same digit in different places within one number
🔍 Comparing Two 4s in ONE Number
This number has TWO 4s. Let's compare them!
400 is 10 times the value of 40
40 is 1/10 the value of 400
✏️ Your Turn: Compare the Two 2s
1. What is the VALUE of the first 2?
2. What is the VALUE of the second 2?
3. Write two comparison statements.
First 2: 0.2 (tenths) | Second 2: 0.02 (hundredths)
0.2 is 10 times the value of 0.02
0.02 is 1/10 the value of 0.2
The ×100 Pattern 💯
What happens when we move TWO places?
💯 Moving TWO Places = ×100
If ONE place is ×10, then TWO places is ×10 × 10 = ×100!
7 is 100 times the value of 0.07
0.07 is 1/100 the value of 7
🔍 Compare the Two 7s
These 7s are TWO places apart!
0.07 is 100 times the value of 0.0007
0.0007 is 1/100 the value of 0.07
Same Digit, TWO Numbers 🔀
Comparing the same digit across different numbers
🔀 Comparing Across Two Numbers
Compare the value of the digit 5 in each number:
The value of the 5 in 75,249 is 10 times the value of the 5 in 568.3.
The value of the 5 in 568.3 is 1/10 the value of the 5 in 75,249.
✏️ Your Turn: Compare the 9s
Compare the value of the digit 9 in each number:
First 9 = 90,000 (ten thousands)
Second 9 = 900 (hundreds)
The 9 in 97,062.34 is 100 times the value of the 9 in 128,913.745
Find the Number! 🎯
Multiple choice challenges to test your skills
🎯 Find the Number!
Which number has a digit 6 with a value 10 times as much as the 6 in 86,932.4?
First: What's the value of 6 in 86,932.4? → 6,000
So we need a 6 worth 60,000!
🎯 Find the Number!
Which number has a digit 9 with a value 1/10 as much as the 9 in 321,495.67?
First: What's the value of 9 in 321,495.67? → 90
So we need a 9 worth 9!
🎯 Find the Number!
Which number has a digit 8 with a value 100 times as much as the 8 in 83,792.1?
First: What's the value of 8 in 83,792.1? → 80,000
So we need an 8 worth 8,000,000!
Mixed Practice 🌟
Put it all together!
⚡ Quick Fire Round!
📖 Word Problem
There are 200 sailboats on the lake today.
If 1/10 of the boats are blue, how many sailboats are blue?
What does "1/10 of 200" mean? How does place value help us solve this?
1/10 of 200 means ÷10
200 ÷ 10 = 20
20 blue sailboats!
📖 Word Problem
There are 3,000 yellow flowers at the park.
If there are 10 times as many red flowers as yellow flowers, how many red flowers are there?
10 times 3,000 means ×10
3,000 × 10 = 30,000
30,000 red flowers!
⭐ Challenge Question
A. The 7 in 56,372.04 has a value 1/10 the value of the 7 in 38,427.95
B. The 8 in 138,092.6 has a value 1/10 the value of the 8 in 89,346.02
C. The 4 in 9,048.35 has a value 1/10 the value of the 4 in 60,892.54
A: 7 in 56,372.04 = 70 | 7 in 38,427.95 = 7 → 70 is NOT 1/10 of 7 ❌
B: 8 in 138,092.6 = 8,000 | 8 in 89,346.02 = 80,000 → 8,000 IS 1/10 of 80,000 ✅
C: 4 in 9,048.35 = 40 | 4 in 60,892.54 = 0.04 → 40 is NOT 1/10 of 0.04 ❌
Answer: B
Place Value Pro!
You now understand how digits change value as they move through place value positions. Remember: moving LEFT multiplies by 10, moving RIGHT divides by 10. You can compare any digits using "10 times," "1/10," "100 times," and "1/100"!