Decimal Shift Slides Grade 5 Mathematics • Place Value Lab
Patterns & Powers of 10
The Decimal Power Shift
Discover what really happens to tenths and hundredths when we multiply by 100 and 1,000.
10²
× 100
Shifts 2 places left
10³
× 1,000
Shifts 3 places left
Value Jumps
100× & 1,000× greater
The Base-Ten Engine
Concept 1
Multiplying by 100
\( 100 = 10 \times 10 \) (2 factors of 10)
Every digit shifts 2 places to the left. Its value becomes 100 times larger!
Multiplying by 1,000
\( 1,000 = 10 \times 10 \times 10 \) (3 factors of 10)
Every digit shifts 3 places to the left. Its value becomes 1,000 times larger!
Place Value Shift Direction
Thousands
Hundreds
Tens
Ones
Notice: As digits move left into higher place values, empty places to the right before the decimal must be filled with zeros as placeholders!
Place Value Observation Step 1 of 5
Tenths in Motion: Multiplying \( 0.4 \)
Case Study: 0.4
\( 0.4 \times 100 = 40 \) (Shifted 2 positions left)
4 tenths → 4 tens
Hundreds
Tens
Ones
. Tenths
Hundredths
0
. 4
4
0
.
\( 0.4 \times 1,000 = 400 \) (Shifted 3 positions left)
4 tenths → 4 hundreds
Hundreds
Tens
Ones
. Tenths
Hundredths
4
0
0
.
Where did the zeros come from? They fill the empty ones and tens places to hold the value!
Hundredths in Motion: Multiplying \( 0.35 \)
Case Study: 0.35
Step 1: Two places left
\( 0.35 \times 100 = 35 \)
3 tenths shifts 2 places → 3 tens
5 hundredths shifts 2 places → 5 ones
Result is a whole number: 35
Step 2: Three places left
\( 0.35 \times 1,000 = 350 \)
3 tenths shifts 3 places → 3 hundreds
5 hundredths shifts 3 places → 5 tens
Place holder 0 fills the empty ones
Needs 1 placeholder zero: 350
Compare: \( 0.35 \times 100 = 35 \) vs \( 0.35 \times 1,000 = 350 \) Step 2 of 5
Misconception Alert: The "Just Add Zeros" Trap
Critical Thinking
Common Mistake
\( 0.4 \times 100 = 0.400 \) ?
"100 has two zeros, so I just stick two zeros on the end!"
Why it's WRONG:
\( 0.400 \) is exactly equal in value to \( 0.4 \)! You didn't make it 100 times bigger at all!
Mathematical Truth
\( 0.4 \times 100 = 40 \)
The digits shift places! The decimal point stays anchored, or appears to shift 2 places right.
The Golden Rule:
Multiplying by 100 makes the quantity 100 times bigger. 4 tenths becomes 4 tens (40)!
Avoid the zero trap by tracking place values! Step 3 of 5
Quick Fire: Place Value Showdown
Whole Class Check
Round 1 (Tenths)
\( 0.8 \times 100 \)
Digit 8 starts in tenths. Shifts 2 places left.
Answer: 80
Round 2 (Hundredths)
\( 0.09 \times 1,000 \)
Digit 9 starts in hundredths. Shifts 3 places left.
Answer: 90
Round 3 (Mixed Decimal)
\( 1.25 \times 1,000 \)
All three digits shift 3 places left.
Answer: 1,250
Ready for independent practice? Grab your Decimal Shift Worksheet !
Shift Count: ×100 → 2 left | ×1,000 → 3 left
Decimal Shift Worksheet Grade 5 Math Powers of Ten Unit
Decimal Power Shift: Multiplying by 100 and 1,000
Practice & Exploration
Worksheet 5.NBT.2
Name:
Date:
Score: / 25
1 Part 1: Track the Digits on the Place Value Chart
Write digits in the chart & record final product
Problem A: \( 0.7 \times 100 \) (Multiply by 100 = Shift digits 2 places left) Final Product:
Thousands Hundreds Tens Ones . Tenths Hundredths Start: 0.7 0 7 × 100 .
Problem B: \( 0.24 \times 1,000 \) (Multiply by 1,000 = Shift digits 3 places left) Final Product:
Thousands Hundreds Tens Ones . Tenths Hundredths Start: 0.24 0 2 4 × 1,000 .
2 Part 2: The Multiplier Matrix
Compare products across powers of 10
| Original Decimal | × 10
3 Part 3: Rapid Fluency Practice
Calculate each product using mental place-value shifts
1. \( 0.3 \times 100 = \)
2. \( 0.3 \times 1,000 = \)
3. \( 0.65 \times 100 = \)
4. \( 0.65 \times 1,000 = \)
5. \( 0.04 \times 100 = \)
6. \( 0.04 \times 1,000 = \)
Place Value Rule: Count the zeros in the multiplier (100 = 2, 1,000 = 3) to count digit shifts to the left. Page 1 of 2
Page 2
Reasoning, Error Analysis & Metric Applications
Name:
4 Part 4: Missing Power & Unknown Value Puzzle
Fill in with 100, 1,000, or the missing decimal
A. \( 0.8 \times \) \( = 800 \) Shift 3
B. \( 0.27 \times \) \( = 27 \) Shift 2
C. \( \times 100 = 49 \) Original?
Decimal Shift Teacher Guide Teacher Guide Grade 5 • Standard CCSS.MATH.CONTENT.5.NBT.A.2
Decimal Power Shift: Facilitation Guide
Instructional Notes
60-Minute Lesson
Core Standard 5.NBT.A.2 (Powers of 10)
Prior Knowledge Tenths/hundredths notation
Key Vocabulary Shift, power of 10, placeholder
Manipulatives Place value charts, dry-erase
Recommended Pacing & Lesson Arc
10 min • Hook
Slide 1-2: Compare \( 4 \times 100 \) vs \( 0.4 \times 100 \). Introduce the place value machine.
15 min • Direct Demo
Slide 3-4: Model \( 0.4 \) and \( 0.35 \) on live chart. Explicitly count digit jumps left.
20 min • Practice
Worksheet Parts 1-4: Partner collaboration with independent matrix completion.
15 min • Debrief
Parts 5-6: Error detective discussion, myth busting, and exit ticket check.
High-Impact Questioning & Teacher Prompts
Q1: "When we multiply \( 0.4 \) by 100, why doesn't the answer become \( 0.400 \)?"
Target Response: "\( 0.400 \) and \( 0.4 \) are equivalent decimals having the same value. Multiplying by 100 makes a number 100 times greater, shifting 4 tenths into 4 tens (40)."
Q2: "What determines how many places the digits shift?"
Target Response: "The number of factors of 10. Multiplying by \( 100 = 10 \times 10 \) shifts digits 2 places left; \( 1,000 = 10 \times 10 \times 10 \) shifts digits 3 places left."
Q3: "Why do we write zeros after the digits in \( 0.4 \times 100 = 40 \) and \( 0.4 \times 1,000 = 400 \)?"
Target Response: "The zeros are placeholders. Without the zero in the ones place, 4 tens would just look like 4 ones."
Key Misconceptions & How to Correct Them
Misconception: "Tack On Zeros"
Students carry over whole number intuition (\( 5 \times 100 = 500 \)) and write \( 0.7 \times 100 = 0.700 \).
Fix: Write 0.700 on tenths/hundredths grid to prove it is identical in size to 0.7. Emphasize value increase.
Misconception: Decimal Point Shift Direction
Students confuse digits shifting left with the decimal point appearing to move right .
Fix: Keep the decimal point rigidly anchored on the board between ones and tenths; slide digit cards to the left.
Place Value Mastery • Grade 5 Module 1 Page 1 of 2
Answer Key
Decimal Shift Worksheet • Solutions & Explanations
Full Worked Solutions
