Rule #1 — Multiplying by a Power of 10:
1. Count the zeros in the power of 10
2. Move the decimal point that many places to the RIGHT →
3. Fill empty spots with zeros
Examples:
• 1.2 × 10 = 12 (moved 1 right)
• 1.2 × 100 = 120 (moved 2 right)
• 1.2 × 1,000 = 1,200 (moved 3 right)
Multiplying makes numbers BIGGER → decimal goes RIGHT
Decimals × Powers of 10
Multiply & Divide — Move That Decimal!
📚
Subject
Math
⏱️
Duration
60+ min
🎯
Standard
5.NBT.A.2
📋 Standards & Objectives
📜Standards
5.NBT.A.2Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10.
5.NBT.A.1Recognize that in a multi-digit number, a digit in one place represents 10 times as much as the place to its right and 1/10 of the place to its left.
🎯SWBAT
- Multiply a decimal by 10, 100, and 1,000 by moving the decimal point to the right
- Divide a decimal by 10, 100, and 1,000 by moving the decimal point to the left
- Count the zeros in the power of 10 to determine how many places to move the decimal
- Apply the multiply/divide rules quickly and accurately to solve problems
📖 Key Vocabulary
📝Power of 10
A number you get by multiplying 10 by itself. The powers of 10 are 10, 100, 1,000, 10,000, and so on.
10 = one power of 10 (10 × 1)
100 = two powers of 10 (10 × 10)
1,000 = three powers of 10 (10 × 10 × 10)
📝Decimal Point
The dot in a number that separates the whole number part from the fractional part. In 3.25, the dot between 3 and 2 is the decimal point.
In 4.7, the decimal point separates the 4 (ones) from the 7 (tenths).
In 0.05, the decimal point tells us the 5 is in the hundredths place.
📝Place Value
The value of a digit based on its position in a number. Moving left = 10× bigger. Moving right = 10× smaller.
In 555, the first 5 = 500, the second 5 = 50, and the third 5 = 5. Same digit, different place values.
In 2.34, the 3 has a place value of 3 tenths, and the 4 has a place value of 4 hundredths.
📝Product
The answer you get when you multiply two numbers together.
The product of 6 × 10 is 60.
When we find 1.5 × 100, the product is 150.
🚀 What You Already Know
You're better at this than you think!
You already know how to multiply whole numbers by powers of 10. Today we're going to use that exact same skill — just with decimals.
Here's the Secret
Multiplying and dividing decimals by powers of 10 is actually easier than what you already do with whole numbers. All you have to do is move the decimal point. That's it. By the end of today, you'll be able to do these problems in your head — faster than you can type them into a calculator.
👨🏫 Whole Numbers × 10
Let's start with what you already crush
7
×
10
=
70
What happened? We just added 1 zero to the 7.
8
×
10
=
80
25
×
10
=
250
× 10 → add 1 zero. You already know this!
👨🏫 Whole Numbers × 100 and × 1,000
Count the zeros in the power of 10!
7
×
100
=
700
← 2 zeros added
7
×
1,000
=
7,000
← 3 zeros added
80
×
20
=
1,600
← 8 × 2 = 16, then add 2 zeros
The Pattern
When you multiply a whole number by a power of 10, you add zeros. The number of zeros you add = the number of zeros in the power of 10.
👨🏫 The "Count the Zeros" Rule
This is the rule you already use
× 10
1 zero
5 × 10 = 50
× 100
2 zeros
5 × 100 = 500
× 1,000
3 zeros
5 × 1,000 = 5,000
Zeros in the power of 10 = zeros you add to your answer
✅ Quick Check: Whole Numbers
Solve these in your head!
9 × 100 = ?
900 — 100 has 2 zeros, so add 2 zeros to 9
42 × 10 = ?
420 — 10 has 1 zero, so add 1 zero to 42
6 × 1,000 = ?
6,000 — 1,000 has 3 zeros, so add 3 zeros to 6
🔄 The Big Connection
From adding zeros to moving the decimal
You just proved: when you multiply by a power of 10, the number gets bigger. The zeros in the power of 10 tell you how much bigger.
But what about decimals?
You can't just "add zeros" to 1.2 — that would give you 1.200, which is the same number! Instead, with decimals we move the decimal point. The number of zeros in the power of 10 tells you how many places to move.
Whole Numbers
Count zeros → add that many zeros
Decimals
Count zeros → move decimal that many places
Same idea. Different move. Let's see it in action.
👨🏫 Decimal × 10
Watch what happens to the decimal point
1.2
×
10
=
12
10 has 1 zero → move the decimal point 1 place RIGHT
1.2 → 12.
The decimal jumped 1 spot to the right!
3.45
×
10
=
34.5
3.45 → 34.5 (decimal moved 1 place right)
👨🏫 Decimal × 100
100 has 2 zeros → move 2 places
1.2
×
100
=
120
1.2 →→ 120.
Decimal jumped 2 spots right! (We added a 0 to fill the empty place)
0.56
×
100
=
56
4.357
×
100
=
435.7
👨🏫 Decimal × 1,000
1,000 has 3 zeros → move 3 places
1.2
×
1,000
=
1,200
1.2 →→→ 1200.
Decimal jumped 3 spots right! (Added zeros to fill empty places)
0.045
×
1,000
=
45
2.5
×
1,000
=
2,500
⭐ Rule #1: Multiply by a Power of 10
Your new best friend
MULTIPLY = Move Decimal RIGHT
Count the zeros in the power of 10.
Move the decimal point that many places to the RIGHT →
× 10
→ 1 place
× 100
→→ 2 places
× 1,000
→→→ 3 places
If you run out of digits, fill with zeros! (e.g., 1.2 × 100 = 120)
📓 Write This Down
Write this in your notebook!
Key Terms
Multiply
Power of 10
Decimal RIGHT
Notes
👨🏫 More Multiply Examples
Let's see more in action
0.7 × 10 = ?
7
1 zero → move 1 right: 0.7 → 7
0.03 × 100 = ?
3
2 zeros → move 2 right: 0.03 → 3
12.5 × 10 = ?
125
1 zero → move 1 right: 12.5 → 125
0.006 × 1,000 = ?
6
3 zeros → move 3 right: 0.006 → 6
✅ Quick Check: Multiply
Show me a thumbs up when you've got it!
When you MULTIPLY a decimal by a power of 10, which way does the decimal move?
👈 LEFT or RIGHT 👉
RIGHT → → →
Multiply = bigger number = decimal moves RIGHT
🔄 Now Let's Go the Other Way
Multiplying makes bigger... dividing makes...?
You just learned: Multiply by a power of 10 → decimal moves RIGHT (number gets bigger).
So what about dividing?
Division is the opposite of multiplication. If multiply moves the decimal RIGHT, then divide moves it... LEFT. Same counting rule. Opposite direction.
× (Multiply)
Decimal → RIGHT
Number gets BIGGER
÷ (Divide)
Decimal ← LEFT
Number gets SMALLER
👨🏫 Decimal ÷ 10
10 has 1 zero → move 1 place LEFT
1.2
÷
10
=
0.12
1.2 ← 0.12
The decimal jumped 1 spot to the LEFT!
34.5
÷
10
=
3.45
250
÷
10
=
25
👨🏫 Decimal ÷ 100
100 has 2 zeros → move 2 places LEFT
45
÷
100
=
0.45
45. ←← 0.45
Decimal jumped 2 spots LEFT! (Added a 0 in front)
3.7
÷
100
=
0.037
620
÷
100
=
6.2
👨🏫 Decimal ÷ 1,000
1,000 has 3 zeros → move 3 places LEFT
500
÷
1,000
=
0.5
500. ←←← 0.5
Decimal jumped 3 spots LEFT!
7
÷
1,000
=
0.007
82.6
÷
1,000
=
0.0826
⭐ Rule #2: Divide by a Power of 10
The opposite of Rule #1
DIVIDE = Move Decimal LEFT
Count the zeros in the power of 10.
Move the decimal point that many places to the ← LEFT
÷ 10
← 1 place
÷ 100
←← 2 places
÷ 1,000
←←← 3 places
If you run out of digits, add zeros in front! (e.g., 7 ÷ 1,000 = 0.007)
📓 Write This Down
Write this in your notebook!
Key Terms
Divide
Power of 10
Decimal LEFT
Notes
Rule #2 — Dividing by a Power of 10:
1. Count the zeros in the power of 10
2. Move the decimal point that many places to the LEFT ←
3. Fill empty spots with zeros
Examples:
• 1.2 ÷ 10 = 0.12 (moved 1 left)
• 45 ÷ 100 = 0.45 (moved 2 left)
• 500 ÷ 1,000 = 0.5 (moved 3 left)
Dividing makes numbers SMALLER → decimal goes LEFT
1. Count the zeros in the power of 10
2. Move the decimal point that many places to the LEFT ←
3. Fill empty spots with zeros
Examples:
• 1.2 ÷ 10 = 0.12 (moved 1 left)
• 45 ÷ 100 = 0.45 (moved 2 left)
• 500 ÷ 1,000 = 0.5 (moved 3 left)
Dividing makes numbers SMALLER → decimal goes LEFT
👨🏫 More Divide Examples
Practice with the reveal buttons
8.4 ÷ 10 = ?
0.84
1 zero → move 1 left: 8.4 → 0.84
2 ÷ 100 = ?
0.02
2 zeros → move 2 left: 2 → 0.02
350 ÷ 100 = ?
3.5
2 zeros → move 2 left: 350 → 3.50 → 3.5
43 ÷ 1,000 = ?
0.043
3 zeros → move 3 left: 43 → 0.043
✅ Quick Check: Divide
Make sure you've got both rules!
When you DIVIDE a decimal by a power of 10, which way does the decimal move?
👈 LEFT or RIGHT 👉
← ← ← LEFT
Divide = smaller number = decimal moves LEFT
Memory Trick
Multiply = More = Move RIGHT →
Divide = Decrease = Decimal LEFT ←
💬 Turn & Talk
🤔Discuss with a Partner
Your friend says: "I multiplied 3.5 × 100 and got 3.500." What did they do wrong? What should the answer be?
Sentence starter: "The mistake was ___ because when you multiply by 100, you should ___. The correct answer is ___."
They just added zeros to the end — but adding zeros after a decimal doesn't change the value! Instead, move the decimal point 2 places RIGHT: 3.5 → 35 → 350
👥 We Do Together: Multiply Set
Solve with your partner, then check!
2.4 × 10
24
1 zero → 1 place right
0.36 × 100
36
2 zeros → 2 places right
5.09 × 10
50.9
1 zero → 1 place right
0.004 × 1,000
4
3 zeros → 3 places right
7.1 × 100
710
2 zeros → 2 places right (add a 0)
0.52 × 10
5.2
1 zero → 1 place right
👥 We Do Together: Divide Set
Solve with your partner, then check!
7.6 ÷ 10
0.76
1 zero → 1 place left
56 ÷ 100
0.56
2 zeros → 2 places left
91 ÷ 10
9.1
1 zero → 1 place left
4 ÷ 1,000
0.004
3 zeros → 3 places left (add zeros)
230 ÷ 100
2.3
2 zeros → 2 places left
15.8 ÷ 10
1.58
1 zero → 1 place left
👥 We Do Together: Mixed Set
Watch out — some multiply, some divide!
6.3 × 100
630
× = RIGHT → 2 places
49 ÷ 10
4.9
÷ = LEFT ← 1 place
0.8 ÷ 100
0.008
÷ = LEFT ← 2 places
0.025 × 1,000
25
× = RIGHT → 3 places
3,200 ÷ 1,000
3.2
÷ = LEFT ← 3 places
14.7 × 10
147
× = RIGHT → 1 place
✅ Quick Check: Both Rules
Two questions — thumbs up or thumbs down!
True or False: 4.5 × 100 = 450
TRUE!
2 zeros → move 2 right: 4.5 → 45 → 450
True or False: 72 ÷ 100 = 7.2
FALSE!
2 zeros → move 2 LEFT: 72 → 7.2 → 0.72. They only moved 1 place!
👥 Tricky Ones — Watch Out!
Common mistakes to avoid
⚠️Tricky: Where's the decimal in a whole number?
Every whole number has a decimal point — it's just invisible! 45 = 45. The decimal hides at the END of a whole number.
So: 45 ÷ 100 → start at 45. and move 2 left → 0.45
⚠️Tricky: Need to add placeholder zeros!
When you run out of digits while moving, add zeros to fill the gaps.
Example: 3 ÷ 1,000 → need to move 3 left from 3. → 0.3 → 0.03 → 0.003
⚠️Tricky: Don't just slap zeros on the end!
3.5 × 100 ≠ 3.500. Adding zeros after the decimal doesn't change the value. You need to move the decimal.
Correct: 3.5 × 100 → move 2 right → 350
👥 See the Pattern
Fill in this table together
| Start | × 10 | × 100 | × 1,000 | ÷ 10 | ÷ 100 | ÷ 1,000 |
|---|---|---|---|---|---|---|
| 4.5 | 45 | 450 | 4,500 | 0.45 | 0.045 | 0.0045 |
| 0.8 | 8 | 80 | 800 | 0.08 | 0.008 | 0.0008 |
| 12.35 | 123.5 | 1,235 | 12,350 | 1.235 | 0.1235 | 0.01235 |
Notice: going RIGHT (multiply) makes numbers bigger. Going LEFT (divide) makes them smaller. Same digits, different decimal position!
🔄 Your Turn Is Coming!
Let's review before you fly solo
You just practiced both rules with a partner. Now you'll do them on your own. Here's your cheat sheet:
Rule #1: MULTIPLY
Decimal → RIGHT
Count the zeros.
Move that many places RIGHT.
Fill empty spots with zeros.
Rule #2: DIVIDE
Decimal ← LEFT
Count the zeros.
Move that many places LEFT.
Fill empty spots with zeros.
3 steps every time: (1) Multiply or divide? (2) Count zeros. (3) Move the decimal.
🔍 You Try: Set 1 — Multiply
Do these on your whiteboard — all multiply!
3.6 × 10
36
0.47 × 100
47
0.9 × 1,000
900
15.2 × 10
152
0.012 × 100
1.2
2.08 × 100
208
🔍 You Try: Set 2 — Divide
Do these on your whiteboard — all divide!
9.3 ÷ 10
0.93
84 ÷ 100
0.84
60 ÷ 1,000
0.06
125 ÷ 10
12.5
5 ÷ 100
0.05
7.2 ÷ 100
0.072
🔍 You Try: Mixed Set
Multiply AND divide — read carefully!
0.63 × 10
6.3
310 ÷ 100
3.1
0.005 × 1,000
5
86.4 ÷ 10
8.64
4.01 × 100
401
19 ÷ 1,000
0.019
🔍 Challenge Round
Can you do these trickier ones?
0.1 × 10
1
0.1 → 1.0 → 1
0.01 × 100
1
0.01 → 0.1 → 1
1 ÷ 10
0.1
1. → 0.1
1 ÷ 1,000
0.001
1. → 0.1 → 0.01 → 0.001
0.002 × 100
0.2
0.002 → 0.02 → 0.2
4,500 ÷ 1,000
4.5
4500. → 450. → 45. → 4.5
⭐ The Two Big Rules — Anchor Chart
This is everything you need to remember
MULTIPLY
Decimal → RIGHT
Step 1: Am I multiplying? YES.
Step 2: Count the zeros.
Step 3: Move decimal that many places RIGHT.
DIVIDE
Decimal ← LEFT
Step 1: Am I dividing? YES.
Step 2: Count the zeros.
Step 3: Move decimal that many places LEFT.
Memory Trick: Multiply = More = Move RIGHT → | Divide = Decrease = Decimal LEFT ←
📓 Summary Note
Last thing in your notebook for today!
Write 1 Sentence
In the bottom of your notebook page, write one sentence explaining the two rules for multiplying and dividing decimals by powers of 10. Include which direction the decimal point moves for each operation.
🎫 Exit Ticket
Show what you know!
1️⃣Multiply
6.7 × 100
Move 2 right: 6.7 → 67 → 670
2️⃣Divide
52 ÷ 1,000
Move 3 left: 52. → 5.2 → 0.52 → 0.052
3️⃣Mixed
0.09 × 1,000
Move 3 right: 0.09 → 0.9 → 9 → 90