Tenth and Hundredths Worksheet featuring exercises on decimal place value and shading grids.

Problem Analysis:

The worksheet focuses on understanding tenths and hundredths using grids. Each question involves identifying or shading parts of a grid to represent fractions in decimal form. Let's solve each part step by step.

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1. What is the value of the shaded area?

#### Grid Description:
- The grid has 10 equal vertical sections.
- 2 sections are shaded.

#### Solution:
- Since there are 10 sections in total, each section represents \( \frac{1}{10} \) (one tenth).
- Shading 2 sections means \( 2 \times \frac{1}{10} = \frac{2}{10} \).
- In decimal form, \( \frac{2}{10} = 0.2 \).

Answer: \( 0.2 \)

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2. What is the value of the shaded area?

#### Grid Description:
- The grid has 100 small squares (10 rows and 10 columns).
- 30 squares are shaded.

#### Solution:
- Since there are 100 squares in total, each square represents \( \frac{1}{100} \) (one hundredth).
- Shading 30 squares means \( 30 \times \frac{1}{100} = \frac{30}{100} \).
- Simplify \( \frac{30}{100} \) to \( \frac{3}{10} \).
- In decimal form, \( \frac{30}{100} = 0.30 \).

Answer: \( 0.30 \)

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3. What is the value of the shaded area?

#### Grid Description:
- The grid has 10 equal vertical sections.
- 5 sections are shaded.

#### Solution:
- Each section represents \( \frac{1}{10} \).
- Shading 5 sections means \( 5 \times \frac{1}{10} = \frac{5}{10} \).
- Simplify \( \frac{5}{10} \) to \( \frac{1}{2} \).
- In decimal form, \( \frac{5}{10} = 0.5 \).

Answer: \( 0.5 \)

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4. What is the value of the shaded area?

#### Grid Description:
- The grid has 100 small squares.
- 60 squares are shaded.

#### Solution:
- Each square represents \( \frac{1}{100} \).
- Shading 60 squares means \( 60 \times \frac{1}{100} = \frac{60}{100} \).
- Simplify \( \frac{60}{100} \) to \( \frac{3}{5} \).
- In decimal form, \( \frac{60}{100} = 0.60 \).

Answer: \( 0.60 \)

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5. What is the value of the shaded area?

#### Grid Description:
- The grid has 100 small squares.
- 70 squares are shaded.

#### Solution:
- Each square represents \( \frac{1}{100} \).
- Shading 70 squares means \( 70 \times \frac{1}{100} = \frac{70}{100} \).
- Simplify \( \frac{70}{100} \) to \( \frac{7}{10} \).
- In decimal form, \( \frac{70}{100} = 0.70 \).

Answer: \( 0.70 \)

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6. What is the value of the shaded area?

#### Grid Description:
- The grid has 100 small squares.
- 80 squares are shaded.

#### Solution:
- Each square represents \( \frac{1}{100} \).
- Shading 80 squares means \( 80 \times \frac{1}{100} = \frac{80}{100} \).
- Simplify \( \frac{80}{100} \) to \( \frac{4}{5} \).
- In decimal form, \( \frac{80}{100} = 0.80 \).

Answer: \( 0.80 \)

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7. Shade 4 squares. How many hundredths have been shaded?

#### Grid Description:
- The grid has 100 small squares.

#### Solution:
- Each square represents \( \frac{1}{100} \).
- Shading 4 squares means \( 4 \times \frac{1}{100} = \frac{4}{100} \).
- In decimal form, \( \frac{4}{100} = 0.04 \).

Answer: \( 0.04 \)

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8. Shade 4 rows. How many tenths have been shaded?

#### Grid Description:
- The grid has 10 rows.

#### Solution:
- Each row represents \( \frac{1}{10} \).
- Shading 4 rows means \( 4 \times \frac{1}{10} = \frac{4}{10} \).
- Simplify \( \frac{4}{10} \) to \( \frac{2}{5} \).
- In decimal form, \( \frac{4}{10} = 0.4 \).

Answer: \( 0.4 \)

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9. The table below refers to a hundred square grid. Complete the table.

| Shaded Rows | Tenths | Hundredths |
|-------------|--------|------------|
| 1 row | \( \frac{1}{10} \) | \( \frac{10}{100} \) |
| | \( \frac{3}{10} \) | |
| | | \( \frac{50}{100} \) |
| 8 rows | | |

#### Step-by-Step Completion:

1. Second Row:
- Given \( \frac{3}{10} \) in the "Tenths" column.
- Convert \( \frac{3}{10} \) to hundredths: \( \frac{3}{10} = \frac{30}{100} \).
- Fill in the "Hundredths" column: \( \frac{30}{100} \).

2. Third Row:
- Given \( \frac{50}{100} \) in the "Hundredths" column.
- Convert \( \frac{50}{100} \) to tenths: \( \frac{50}{100} = \frac{5}{10} \).
- Fill in the "Tenths" column: \( \frac{5}{10} \).

3. Fourth Row:
- Given 8 rows shaded.
- Each row represents \( \frac{1}{10} \), so 8 rows represent \( 8 \times \frac{1}{10} = \frac{8}{10} \).
- Convert \( \frac{8}{10} \) to hundredths: \( \frac{8}{10} = \frac{80}{100} \).
- Fill in the "Tenths" column: \( \frac{8}{10} \).
- Fill in the "Hundredths" column: \( \frac{80}{100} \).

#### Completed Table:

| Shaded Rows | Tenths | Hundredths |
|-------------|------------|---------------|
| 1 row | \( \frac{1}{10} \) | \( \frac{10}{100} \) |
| | \( \frac{3}{10} \) | \( \frac{30}{100} \) |
| | \( \frac{5}{10} \) | \( \frac{50}{100} \) |
| 8 rows | \( \frac{8}{10} \) | \( \frac{80}{100} \) |

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Final Answers:

1. \( 0.2 \)
2. \( 0.30 \)
3. \( 0.5 \)
4. \( 0.60 \)
5. \( 0.70 \)
6. \( 0.80 \)
7. \( 0.04 \)
8. \( 0.4 \)
9.
- Second row: \( \frac{30}{100} \)
- Third row: \( \frac{5}{10} \)
- Fourth row: \( \frac{8}{10} \) and \( \frac{80}{100} \)

Boxed Final Answer:
\[
\boxed{0.2, 0.30, 0.5, 0.60, 0.70, 0.80, 0.04, 0.4, \frac{30}{100}, \frac{5}{10}, \frac{8}{10}, \frac{80}{100}}
\]