Week 2 - FREE Math Quizzes for NBT & NS - Raffle for Assessment ... - Free Printable

Let's solve each problem on this 5th-grade quiz step by step and explain the solutions.

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Problem 1: Compare whole numbers and decimals using multiplication and fractions

Task: Draw a picture of each value to show how they compare.
The columns are:
- 1 Ten
- 1 One
- 1 Tenth
- 1 Hundredth

We need to draw representations for each place value. Since we can't draw here, I'll describe what should be drawn.

#### Explanation:
- 1 Ten: This is 10 units. You could draw a long rectangle (like a "rod") divided into 10 equal parts, or simply write "10".
- 1 One: A single unit. Draw a small square or circle.
- 1 Tenth: This is 0.1. Represent it as one-tenth of a whole. For example, divide a square into 10 equal parts and shade 1 part.
- 1 Hundredth: This is 0.01. Divide a square into 100 parts (a 10x10 grid) and shade 1 tiny square.

These drawings help students see that:
- 1 Ten = 10 Ones
- 1 One = 10 Tenths
- 1 Tenth = 10 Hundredths

So, 1 Ten = 100 Hundredths, etc.

> ✔ Answer: Drawings should reflect relative sizes: a large block for ten, smaller for one, even smaller for tenth, and tiny for hundredth.

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Problem 2: Multiply and divide by exponents of ten

Solve:

#### Multiplication:
- $ 26.66 \times 10^1 = 26.66 \times 10 = 266.6 $
- $ 26.66 \times 10^2 = 26.66 \times 100 = 2,666 $
- $ 26.66 \times 10^3 = 26.66 \times 1,000 = 26,660 $

#### Division:
- $ 3.5 \div 10^1 = 3.5 \div 10 = 0.35 $
- $ 3.5 \div 10^2 = 3.5 \div 100 = 0.035 $
- $ 3.5 \div 10^3 = 3.5 \div 1,000 = 0.0035 $

> ✔ Answers:
> - $ 26.66 \times 10^1 = 266.6 $
> - $ 26.66 \times 10^2 = 2,666 $
> - $ 26.66 \times 10^3 = 26,660 $
> - $ 3.5 \div 10^1 = 0.35 $
> - $ 3.5 \div 10^2 = 0.035 $
> - $ 3.5 \div 10^3 = 0.0035 $

Rule Reminder:
- Multiplying by $10^n$: Move decimal point n places right.
- Dividing by $10^n$: Move decimal point n places left.

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Problem 3: Read, write, and compare numbers to thousandths

#### Part A: Write in expanded form
Number: 1,950,007.601

Break down each digit by place value:

- 1,000,000 → $1 \times 10^6$
- 900,000 → $9 \times 10^5$
- 50,000 → $5 \times 10^4$
- 0 → $0 \times 10^3$
- 0 → $0 \times 10^2$
- 7 → $7 \times 10^0$
- 0.6 → $6 \times 0.1$
- 0.00 → $0 \times 0.01$
- 0.001 → $1 \times 0.001$

So, expanded form:
> $1,000,000 + 900,000 + 50,000 + 7 + 0.6 + 0.001$
or more precisely:
> $1 \times 1,000,000 + 9 \times 100,000 + 5 \times 10,000 + 7 \times 1 + 6 \times 0.1 + 1 \times 0.001$

✔ Answer:
1,000,000 + 900,000 + 50,000 + 7 + 0.6 + 0.001

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#### Part B: Write in standard form
Given:
$9,000 + 600 + 50 + 0.70 + 0.05 + 0.0080$

Add them:

- Whole numbers: $9,000 + 600 + 50 = 9,650$
- Decimals: $0.70 + 0.05 = 0.75$, then $+ 0.0080 = 0.7580$

So total:
> $9,650 + 0.7580 = 9,650.758$

✔ Answer: 9,650.758

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#### Part C: Compare decimals

1. Six tenths ___ Sixty hundredths

- Six tenths = $0.6$
- Sixty hundredths = $0.60$

But $0.6 = 0.60$, so they are equal.

✔ Answer: $0.6 = 0.60$ → =

2. 5,000.010 ___ 4,999.999

Compare:
- 5,000.010 > 4,999.999 because 5,000 is greater than 4,999.

✔ Answer: >

3. 51.12 ___ 51.115

Compare:
- Both have 51 ones.
- Tenths: both 1 → same
- Hundredths: 2 vs 1 → 2 > 1

So $51.12 > 51.115$

Note: $51.12 = 51.120$, which is greater than 51.115

✔ Answer: >

4. 789,889.978 ___ 779,898.877

Compare whole number parts:
- 789,889 vs 779,898
- 789,889 > 779,898 → so the first number is larger

✔ Answer: >

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✔ Final Answers Summary:

#### Problem 1:
Drawings required:
- 1 Ten: large block (10 units)
- 1 One: single unit
- 1 Tenth: 1/10 of a unit (e.g., shaded 1 of 10 parts)
- 1 Hundredth: 1/100 of a unit (e.g., 1 of 100 tiny squares)

#### Problem 2:
- $26.66 \times 10^1 = 266.6$
- $26.66 \times 10^2 = 2,666$
- $26.66 \times 10^3 = 26,660$
- $3.5 \div 10^1 = 0.35$
- $3.5 \div 10^2 = 0.035$
- $3.5 \div 10^3 = 0.0035$

#### Problem 3:
- Expanded form: 1,000,000 + 900,000 + 50,000 + 7 + 0.6 + 0.001
- Standard form: 9,650.758
- Comparisons:
- Six tenths = Sixty hundredths → =
- 5,000.010 > 4,999.999 → >
- 51.12 > 51.115 → >
- 789,889.978 > 779,898.877 → >

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