Decimal Multiplication Student Test
Chapter Test: Chapter 5 (Form B)
Multiplying Decimals & Powers of Ten
Name:
Date:
Which expression gives the best estimated product for 3.88 × 19?
A 3 × 15
C 4 × 20
B 3 × 20
D 4 × 25
Find the product.
0.7 × 102 =
Match each expression to its product.
| 24.5 × 10 |
24.5 × 0.01 |
0.245 × 100 |
2.45 × 0.1 |
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0.0245 0.245 2.45 24.5 245 2,450
Part A Shade the decimal grid to show 0.23 × 4.
Part B Use your model to find the product.
0.23 × 4 =
Grade 5 Mathematics • Chapter 5 Test Page 1
Chapter Test: Chapter 5 (Form B)
Name: Date:
A baker uses 4.8 cups of flour for each batch of bread. The baker makes 6 batches.
About how many cups of flour does the baker use in all?
Select the most reasonable estimate.
A 24 cups
C 30 cups
B 25 cups
D 36 cups
Find the product.
0.84 × 6 =
Show your work
Which equation is represented by the model?
A 0.7 × 0.3 = 0.21
B 0.7 × 3.0 = 2.1
C 0.7 × 0.3 = 0.79
D 0.7 × 3.0 = 21
Grade 5 Mathematics • Chapter 5 Test Page 2
Chapter Test: Chapter 5 (Form B)
Name: Date:
Part A Shade the decimal grid to show 0.6 × 0.4.
Part B Use your model to find the product.
0.6 × 0.4 =
Part A Complete the area model to help you find 4.7 × 3.2.
3.0
0.7
0.14 0.2 0.7 0.8 2.1 3.0 4.0 12.0 15.04
Part B Find the product.
4.7 × 3.2 =
Grade 5 Mathematics • Chapter 5 Test Page 3
Chapter Test: Chapter 5 (Form B)
Name: Date:
Fill in the blanks to find 1.06 × 4.3.
1.06 × 4.3 = 106 × 0.01 × 43 ×
= 106 ×
× 0.01 × 0.1
= (
×
) × (0.01 × 0.1)
=
×
So, 1.06 × 4.3 =
Find the product.
0.7 × 4.2 =
Show your calculation steps here
Double check decimal placement in your final product
Grade 5 Mathematics • Chapter 5 Test Page 4
Decimal Multiplication Answer Key
Teacher Resource
Chapter 5 Test: Form B Answer Key
Grade 5 • Multiplying Decimals & Powers of Ten
Total Points: 20 pts
Standards: 5.NBT.A.2, 5.NBT.B.7
- Estimation: 3.88 × 19 1 pt
Correct: (C) 4 × 20
Rationale: 3.88 rounds to 4, and 19 rounds to 20. Estimated product = 80.
- Powers of 10: 0.7 × 102 1 pt
Product = 70
Rationale: Multiplying by 102 (100) shifts digits 2 places left (decimal moves 2 places right).
- Matching Decimal Operations 4 pts (1 pt each)
| 24.5 × 10 |
24.5 × 0.01 |
0.245 × 100 |
2.45 × 0.1 |
| 245 |
0.245 |
24.5 |
0.245 |
Note: Distractors in bank (0.0245 and 2,450) remain unused. Note that both 24.5 × 0.01 and 2.45 × 0.1 yield 0.245.
- Decimal Grid Model: 0.23 × 4 2 pts (1 pt Part A, 1 pt Part B)
Part A: Student shades exactly 92 hundredths squares (4 groups of 23 hundredths).
Part B: 0.23 × 4 = 0.92
Accept shading done continuously or grouped in 4 distinct blocks of 23 squares.
- Word Problem Estimation 1 pt
Correct: (C) 30 cups
Rationale: 4.8 cups rounds to 5 cups. 5 × 6 batches = 30 cups.
- Multiplication: 0.84 × 6 2 pts (1 pt method, 1 pt product)
Product = 5.04
Steps: 84 × 6 = 504. Two decimal places in factor 0.84 gives 2 decimal places in product: 5.04.
Grade 5 Mathematics • Chapter 5 Test Key Page 1 of 2
Chapter 5 Test: Form B Answer Key (Continued) Items 7 – 11 & Scoring Guidance
- Model Identification 1 pt
Correct: (A) 0.7 × 0.3 = 0.21
Rationale: 7 horizontal tenths (0.7) and 3 vertical tenths (0.3) intersect at 21 hundredths (0.21).
- Decimal Grid: 0.6 × 0.4 2 pts (1 pt Part A, 1 pt Part B)
Part A: Model shows 6 rows (0.6) and 4 columns (0.4) with overlapping double-shaded region.
Part B: 0.6 × 0.4 = 0.24 (24 hundredths in overlap).
- Area Model: 4.7 × 3.2 3 pts (2 pts Part A, 1 pt Part B)
3.0
0.2
4.0
12.0
0.8
0.7
2.1
0.14
Part A: Top label: 0.2; Left label: 4.0.
Partial products inside: 12.0, 0.8, 2.1, 0.14.
Part B: Sum of partial products:
12.0 + 0.8 + 2.1 + 0.14 = 15.04
- Properties Decomposition: 1.06 × 4.3 2 pts
1.06 × 4.3 = 106 × 0.01 × 43 × 0.1
= 106 × 43 × 0.01 × 0.1
= (106 × 43) × (0.01 × 0.1)
= 4,558 × 0.001
So, 1.06 × 4.3 = 4.558
- Standard Algorithm: 0.7 × 4.2 2 pts (1 pt algorithm, 1 pt product)
Product = 2.94
Work: 42 × 7 = 294. Total decimal places = 1 + 1 = 2 places. Move decimal 2 places from right: 2.94.
Common Student Misconceptions & Remediation Tips
Decimal Point Placement: Students frequently align decimal points when multiplying (like addition) rather than counting total decimal places in factors. Revisit place value reasoning (tenths × tenths = hundredths).
Powers of 10 vs. Decimals: Distinguish multiplying by 10 (moves decimal right) versus multiplying by 0.1 or 0.01 (moves decimal left). Remind students that multiplying by 0.1 is equivalent to dividing by 10.
Grade 5 Mathematics • Chapter 5 Test Key Page 2 of 2