Printables - Decimals in Expanded Form | HP® Official Site - Free Printable
Educational worksheet: Printables - Decimals in Expanded Form | HP® Official Site. Download and print for classroom or home learning activities.
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Step-by-step solution for: Printables - Decimals in Expanded Form | HP® Official Site
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Show Answer Key & Explanations
Step-by-step solution for: Printables - Decimals in Expanded Form | HP® Official Site
Absolutely! Let’s solve the worksheet “Decimals in Expanded Form” step by step.
---
We are converting standard form decimals into two types of expanded forms:
1. Expanded form (addition only):
Break the number into the sum of its place values.
Example: `6.342 = 6 + 0.3 + 0.04 + 0.002`
2. Expanded form (addition and multiplication):
Show each digit multiplied by its place value fraction.
Example: `6.342 = 6×1 + 3×¹/₁₀ + 4×¹/₁₀₀ + 2×¹/₁₀₀₀`
---
Let’s fill in the blanks row by row.
---
- Expanded form (addition only):
→ 2 + 0.6
- Expanded form (addition and multiplication):
→ Given: `2 × 1 + 6 × ¹/₁₀` → This is already filled correctly.
✔ So, blank to fill: 2 + 0.6
---
- Expanded form (addition only):
→ Given: `5 + 0.3` → Correct.
- Expanded form (addition and multiplication):
→ 5×1 + 3×¹/₁₀
✔ So, blank to fill: 5 × 1 + 3 × ¹/₁₀
---
- Expanded form (addition only):
→ 4 + 0.08
*(Note: The 0 in tenths place is zero, so we skip it)*
- Expanded form (addition and multiplication):
→ Given: `4 × 1 + 8 × ¹/₁₀₀` → Correct.
✔ So, blank to fill: 4 + 0.08
---
- Expanded form (addition only):
→ 6 + 0.2 + 0.07 + 0.009
- Expanded form (addition and multiplication):
→ 6×1 + 2×¹/₁₀ + 7×¹/₁₀₀ + 9×¹/₁₀₀₀
✔ Fill both blanks:
- Addition only: 6 + 0.2 + 0.07 + 0.009
- Addition & multiplication: 6 × 1 + 2 × ¹/₁₀ + 7 × ¹/₁₀₀ + 9 × ¹/₁₀₀₀
---
- Expanded form (addition only):
→ 0.9 + 0.02
*(No whole number part)*
- Expanded form (addition and multiplication):
→ 9×¹/₁₀ + 2×¹/₁₀₀
✔ Fill both blanks:
- Addition only: 0.9 + 0.02
- Addition & multiplication: 9 × ¹/₁₀ + 2 × ¹/₁₀₀
---
→ This corresponds to standard form: 3.507
- Standard form: 3.507
- Expanded form (addition and multiplication):
→ 3×1 + 5×¹/₁₀ + 0×¹/₁₀₀ + 7×¹/₁₀₀₀
But since the hundredths place is 0, we can omit it:
→ 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀
✔ Fill both blanks:
- Standard form: 3.507
- Addition & multiplication: 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀
---
→ Standard form: 1.364
- Standard form: 1.364
- Expanded form (addition only):
→ 1 + 0.3 + 0.06 + 0.004
✔ Fill both blanks:
- Standard form: 1.364
- Addition only: 1 + 0.3 + 0.06 + 0.004
---
- Expanded form (addition only):
→ 8 + 0.005
*(Tenths and hundredths are 0, so we skip them)*
- Expanded form (addition and multiplication):
→ 8×1 + 0×¹/₁₀ + 0×¹/₁₀₀ + 5×¹/₁₀₀₀
→ Simplify: 8 × 1 + 5 × ¹/₁₀₀₀
✔ Fill both blanks:
- Addition only: 8 + 0.005
- Addition & multiplication: 8 × 1 + 5 × ¹/₁₀₀₀
---
→ This means:
- 4 in tenths → 0.4
- 3 in hundredths → 0.03
→ No whole number or thousandths → 0.43
- Standard form: 0.43
- Expanded form (addition only):
→ 0.4 + 0.03
✔ Fill both blanks:
- Standard form: 0.43
- Addition only: 0.4 + 0.03
---
## 📋 Final Completed Table:
| Standard Form | Expanded Form (Addition Only) | Expanded Form (Addition & Multiplication) |
|---------------|----------------------------------------|--------------------------------------------------------------|
| 2.6 | 2 + 0.6 | 2 × 1 + 6 × ¹/₁₀ |
| 5.3 | 5 + 0.3 | 5 × 1 + 3 × ¹/₁₀ |
| 4.08 | 4 + 0.08 | 4 × 1 + 8 × ¹/₁₀₀ |
| 6.279 | 6 + 0.2 + 0.07 + 0.009 | 6 × 1 + 2 × ¹/₁₀ + 7 × ¹/₁₀₀ + 9 × ¹/₁₀₀₀ |
| 0.92 | 0.9 + 0.02 | 9 × ¹/₁₀ + 2 × ¹/₁₀₀ |
| 3.507 | 3 + 0.5 + 0.007 | 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀ |
| 1.364 | 1 + 0.3 + 0.06 + 0.004 | 1 × 1 + 3 × ¹/₁₀ + 6 × ¹/₁₀₀ + 4 × ¹/₁₀₀₀ |
| 8.005 | 8 + 0.005 | 8 × 1 + 5 × ¹/₁₀₀₀ |
| 0.43 | 0.4 + 0.03 | 4 × ¹/₁₀ + 3 × ¹/₁₀₀ |
---
✔ All blanks are now filled correctly!
This exercise helps reinforce understanding of place value and how decimals break down into their component parts — a key skill for math fluency!
Let me know if you’d like a printable version or further practice! 😊
---
🔢 Understanding the Concepts:
We are converting standard form decimals into two types of expanded forms:
1. Expanded form (addition only):
Break the number into the sum of its place values.
Example: `6.342 = 6 + 0.3 + 0.04 + 0.002`
2. Expanded form (addition and multiplication):
Show each digit multiplied by its place value fraction.
Example: `6.342 = 6×1 + 3×¹/₁₀ + 4×¹/₁₀₀ + 2×¹/₁₀₀₀`
---
Let’s fill in the blanks row by row.
---
✔ Row 1: Standard form = 2.6
- Expanded form (addition only):
→ 2 + 0.6
- Expanded form (addition and multiplication):
→ Given: `2 × 1 + 6 × ¹/₁₀` → This is already filled correctly.
✔ So, blank to fill: 2 + 0.6
---
✔ Row 2: Standard form = 5.3
- Expanded form (addition only):
→ Given: `5 + 0.3` → Correct.
- Expanded form (addition and multiplication):
→ 5×1 + 3×¹/₁₀
✔ So, blank to fill: 5 × 1 + 3 × ¹/₁₀
---
✔ Row 3: Standard form = 4.08
- Expanded form (addition only):
→ 4 + 0.08
*(Note: The 0 in tenths place is zero, so we skip it)*
- Expanded form (addition and multiplication):
→ Given: `4 × 1 + 8 × ¹/₁₀₀` → Correct.
✔ So, blank to fill: 4 + 0.08
---
✔ Row 4: Standard form = 6.279
- Expanded form (addition only):
→ 6 + 0.2 + 0.07 + 0.009
- Expanded form (addition and multiplication):
→ 6×1 + 2×¹/₁₀ + 7×¹/₁₀₀ + 9×¹/₁₀₀₀
✔ Fill both blanks:
- Addition only: 6 + 0.2 + 0.07 + 0.009
- Addition & multiplication: 6 × 1 + 2 × ¹/₁₀ + 7 × ¹/₁₀₀ + 9 × ¹/₁₀₀₀
---
✔ Row 5: Standard form = 0.92
- Expanded form (addition only):
→ 0.9 + 0.02
*(No whole number part)*
- Expanded form (addition and multiplication):
→ 9×¹/₁₀ + 2×¹/₁₀₀
✔ Fill both blanks:
- Addition only: 0.9 + 0.02
- Addition & multiplication: 9 × ¹/₁₀ + 2 × ¹/₁₀₀
---
✔ Row 6: Expanded form (addition only) = 3 + 0.5 + 0.007
→ This corresponds to standard form: 3.507
- Standard form: 3.507
- Expanded form (addition and multiplication):
→ 3×1 + 5×¹/₁₀ + 0×¹/₁₀₀ + 7×¹/₁₀₀₀
But since the hundredths place is 0, we can omit it:
→ 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀
✔ Fill both blanks:
- Standard form: 3.507
- Addition & multiplication: 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀
---
✔ Row 7: Expanded form (addition and multiplication) = 1 × 1 + 3 × ¹/₁₀ + 6 × ¹/₁₀₀ + 4 × ¹/₁₀₀₀
→ Standard form: 1.364
- Standard form: 1.364
- Expanded form (addition only):
→ 1 + 0.3 + 0.06 + 0.004
✔ Fill both blanks:
- Standard form: 1.364
- Addition only: 1 + 0.3 + 0.06 + 0.004
---
✔ Row 8: Standard form = 8.005
- Expanded form (addition only):
→ 8 + 0.005
*(Tenths and hundredths are 0, so we skip them)*
- Expanded form (addition and multiplication):
→ 8×1 + 0×¹/₁₀ + 0×¹/₁₀₀ + 5×¹/₁₀₀₀
→ Simplify: 8 × 1 + 5 × ¹/₁₀₀₀
✔ Fill both blanks:
- Addition only: 8 + 0.005
- Addition & multiplication: 8 × 1 + 5 × ¹/₁₀₀₀
---
✔ Row 9: Expanded form (addition and multiplication) = 4 × ¹/₁₀ + 3 × ¹/₁₀₀
→ This means:
- 4 in tenths → 0.4
- 3 in hundredths → 0.03
→ No whole number or thousandths → 0.43
- Standard form: 0.43
- Expanded form (addition only):
→ 0.4 + 0.03
✔ Fill both blanks:
- Standard form: 0.43
- Addition only: 0.4 + 0.03
---
## 📋 Final Completed Table:
| Standard Form | Expanded Form (Addition Only) | Expanded Form (Addition & Multiplication) |
|---------------|----------------------------------------|--------------------------------------------------------------|
| 2.6 | 2 + 0.6 | 2 × 1 + 6 × ¹/₁₀ |
| 5.3 | 5 + 0.3 | 5 × 1 + 3 × ¹/₁₀ |
| 4.08 | 4 + 0.08 | 4 × 1 + 8 × ¹/₁₀₀ |
| 6.279 | 6 + 0.2 + 0.07 + 0.009 | 6 × 1 + 2 × ¹/₁₀ + 7 × ¹/₁₀₀ + 9 × ¹/₁₀₀₀ |
| 0.92 | 0.9 + 0.02 | 9 × ¹/₁₀ + 2 × ¹/₁₀₀ |
| 3.507 | 3 + 0.5 + 0.007 | 3 × 1 + 5 × ¹/₁₀ + 7 × ¹/₁₀₀₀ |
| 1.364 | 1 + 0.3 + 0.06 + 0.004 | 1 × 1 + 3 × ¹/₁₀ + 6 × ¹/₁₀₀ + 4 × ¹/₁₀₀₀ |
| 8.005 | 8 + 0.005 | 8 × 1 + 5 × ¹/₁₀₀₀ |
| 0.43 | 0.4 + 0.03 | 4 × ¹/₁₀ + 3 × ¹/₁₀₀ |
---
✔ All blanks are now filled correctly!
This exercise helps reinforce understanding of place value and how decimals break down into their component parts — a key skill for math fluency!
Let me know if you’d like a printable version or further practice! 😊
Parent Tip: Review the logic above to help your child master the concept of expanded form with decimals.
