Decimal Decoders Worksheet
DECIMAL DECODERS
Dividing Decimals by Decimals Practice
Name:
Date:
Class:
Score:
Division Steps:
1 Shift divisor to whole number • 2 Shift dividend same places • 3 Align decimal up & divide
Problem 1 1-decimal shift
\( 8.16 \div 0.4 \)
Rewritten: ______ ÷ ______
Quotient:
Problem 2 2-decimal shift
\( 6.24 \div 0.12 \)
Rewritten: ______ ÷ ______
Quotient:
Problem 3 Placeholder zero
\( 11.2 \div 0.35 \)
Rewritten: ______ ÷ ______
Quotient:
Problem 4 Real-world context
An art teacher has a spool with 9.75 meters of ribbon. Each student craft project requires 0.75 meters. How many complete craft projects can be made?
Equation: ______ ÷ ______
Projects:
Remember to check your answers using multiplication (\(\text{quotient} \times \text{divisor} = \text{dividend}\)).
Page 1 of 1
Decimal Jumps Practice Worksheet
DECIMAL JUMPS
Place Value & Decimal Movement Foundations
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Date:
Class:
Goal: Master the Shift
Why Do We "Move" the Decimal Point?
We cannot easily split things by a fraction of a group (like dividing by \(0.4\)). To fix this, we multiply both numbers by powers of 10 (\(10\), \(100\), or \(1,000\)). This turns the divisor into a whole number without changing the answer, just like creating equivalent fractions!
Tenths (\(0.1\)) Multiply by \(10\) Jump 1 place right (\(\rightarrow\))
Hundredths (\(0.01\)) Multiply by \(100\) Jump 2 places right (\(\rightarrow\rightarrow\))
Golden Rule Whatever the divisor does... The dividend matches!
Problem 1 \( 4.2 \div 0.7 \)
Step 1: The divisor is \(0.7\) (tenths), so multiply by \(10\) (1 jump right): \(0.7 \rightarrow 7\).
Step 2: Shift dividend \(4.2\) the same 1 place right: \(4.2 \rightarrow 42\).
Step 3: Solve the whole number division: \(42 \div 7\).
Rewritten: 42 ÷ 7
Division Work
Answer:
Problem 2 \( 0.36 \div 0.09 \)
Step 1: Divisor \(0.09\) has 2 decimal places (hundredths). Multiply by \(100\) (2 jumps right): \(0.09 \rightarrow 9\).
Step 2: Shift dividend \(0.36\) two places right: \(0.36 \rightarrow 36\).
Step 3: Solve the division: \(36 \div 9\).
Rewritten: 36 ÷ 9
Division Work
Answer:
Problem 3 \( 8 \div 0.2 \)
Step 1: Divisor \(0.2\) has 1 decimal place. Jump 1 right: \(0.2 \rightarrow 2\).
Step 2: Whole number dividend \(8\) can be written as \(8.0\). When you jump 1 place right, add a placeholder zero: \(8.0 \rightarrow 80\)!
Step 3: Solve: \(80 \div 2\).
Rewritten: 80 ÷ 2
Division Work
Answer:
Part 1: Guided Place Value Foundations Page 1 of 3
DECIMAL JUMPS • PART 2
Apply the Place Value Shift to Solve
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Place Value Checklist: 1. Count divisor places → 2. Jump dividend same places → 3. Fill empty spots with 0 → 4. Line up decimal in answer
Problem 4 Tenths divisor
\( 4.8 \div 0.6 \)
Explanation: The divisor \(0.6\) has 1 decimal place. Multiply both numbers by \(10\) to make the divisor a whole number (\(6\)).
Shift: \(0.6 \times 10 = 6\) and \(4.8 \times 10 = 48\)
Rewritten equation: ______ ÷ ______
Division Work
Answer:
Problem 5 Hundredths divisor
\( 0.75 \div 0.25 \)
Explanation: The divisor \(0.25\) has 2 decimal places. Multiply both numbers by \(100\) to turn \(0.25\) into the whole number \(25\).
Shift: \(0.25 \times 100 = 25\) and \(0.75 \times 100 = 75\)
Rewritten equation: ______ ÷ ______
Division Work
Answer:
Problem 6 Placeholder Zero Alert
\( 3.2 \div 0.08 \)
Explanation: The divisor \(0.08\) has 2 decimal places. We must multiply by \(100\) (2 jumps). The dividend \(3.2\) only has 1 decimal place, so append a zero: \(3.20 \times 100 = 320\)!
Shift: \(0.08 \rightarrow 8\) and \(3.2 \rightarrow 320\)
Rewritten equation: ______ ÷ ______
Division Work
Answer:
Common Misconception Alert: Never jump the dividend more or fewer times than the divisor! The divisor always tells you how many places to jump. Both numbers must jump the exact same number of places.
Part 2: Applying Place Value to Decimal Division Page 2 of 3
DECIMAL JUMPS • PART 3
Independent Practice: Track Your Jumps & Solve
Name:
Your Mission: 1. Count divisor places • 2. Jump dividend by same count • 3. Rewrite without decimals in divisor • 4. Solve!
Problem 7 Tenths
\( 3.5 \div 0.5 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Problem 8 Placeholder 0
\( 5.4 \div 0.09 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Problem 9 Hundredths
\( 0.84 \div 0.04 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Problem 10 Tenths
\( 9.6 \div 0.8 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Problem 11 Placeholder 0
\( 7.2 \div 0.12 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Problem 12 Decimal in Dividend
\( 1.44 \div 0.6 \)
Jumps right: ____ Rewrite: ___ ÷ ___
Quotient:
Quick Check: Did you multiply both numbers by the same power of 10 for every problem?
Yes, verified!
Part 3: Independent Practice with Decimal Jumps Page 3 of 3
Decimal Jumps Instruction Slides
Place Value Math Workshop
DECIMAL JUMPS
Mastering Decimal Division with Place Value Shifts & Powers of 10
Shift Divisors to Whole Numbers • Maintain Value Balance
Slide 1 of 8
The Big Idea
Why Do We Move the Decimal?
Slide 2 of 8
The Problem
Dividing by a partial amount (like 0.4) is hard to visualize and calculate by hand.
\( 8.4 \div 0.4 \) → "How many 0.4s are in 8.4?"
The Secret Solution
Scale both numbers by multiplying by 10, 100, or 1,000 to make the divisor a whole number!
\( 84 \div 4 = 21 \) → Same exact quotient!
Key Concept: Multiplying both parts by the same power of 10 does not change the final answer!
Conceptual Proof
Think of Equivalent Fractions
Slide 3 of 8
Original Division
\( \frac{4.2}{0.7} \)
×
Multiply by \( \frac{10}{10} \) (equals 1)
\( \frac{\times 10}{\times 10} \)
=
Whole Number Form
\( \frac{42}{7} = 6 \)
1
Multiplying a fraction by \( \frac{10}{10} \) is just multiplying by 1. Its true value never changes.
2
Moving a decimal point 1 place right is literally multiplying that number by 10!
Rule: Whatever you do to the bottom (divisor), do to the top (dividend)! Equal Scaling Principle
Rule 1 • Tenths Divisor
One Decimal Place = 1 Jump Right
Slide 4 of 8
Sample Problem: \( 7.56 \div 0.6 \)
Step 1: Inspect Divisor
Look at 0.6. It has 1 decimal place (tenths).
\( 0.6 \xrightarrow{\times 10} 6 \)
Step 2: Match Dividend
Jump the dividend 7.56 the exact same 1 place right.
\( 7.56 \xrightarrow{\times 10} 75.6 \)
Step 3: Solve
Divide using standard long division with divisor 6!
\( 75.6 \div 6 = 12.6 \)
Notice: The dividend may still have a decimal. That is completely okay! 1 Jump Completed
Rule 2 • Hundredths Divisor
Two Decimal Places = 2 Jumps Right
Slide 5 of 8
Sample Problem: \( 0.48 \div 0.04 \)
Divisor: 2 Places
0.04 is hundredths. It takes 2 decimal jumps (\(\times 100\)) to reach the whole number 4.
