Math worksheet for converting fractions to decimals using 100-square grids.

Problem Analysis:

The task involves two main parts:
1. Interpreting shaded grids to determine fractions and decimals.
2. Converting between fractions and decimals.

Let's solve each part step by step.

---

Part 1: Interpreting Shaded Grids

Each grid is divided into 100 smaller squares, representing a hundredth (1/100). The number of shaded squares in each grid corresponds to the numerator of the fraction over 100. We will count the shaded squares for each grid and write the corresponding fraction and decimal.

#### Top Row:
1. First Grid (Green):
- Shaded squares: 10
- Fraction: \( \frac{10}{100} \)
- Decimal: \( 0.10 \)

2. Second Grid (Yellow):
- Shaded squares: 30
- Fraction: \( \frac{30}{100} \)
- Decimal: \( 0.30 \)

3. Third Grid (Red):
- Shaded squares: 89
- Fraction: \( \frac{89}{100} \)
- Decimal: \( 0.89 \)

#### Bottom Row:
4. Fourth Grid (Blue):
- Shaded squares: 5
- Fraction: \( \frac{5}{100} \)
- Decimal: \( 0.05 \)

5. Fifth Grid (Yellow):
- Shaded squares: 100
- Fraction: \( \frac{100}{100} \)
- Decimal: \( 1.00 \)

6. Sixth Grid (Purple):
- Shaded squares: 1
- Fraction: \( \frac{1}{100} \)
- Decimal: \( 0.01 \)

---

Part 2: Converting Between Fractions and Decimals

We need to convert the given fractions to decimals and vice versa.

#### Conversion Table:
1. \( \frac{4}{10} \) to Decimal:
- \( \frac{4}{10} = 0.4 \)

2. Decimal \( 0.8 \) to Fraction:
- \( 0.8 = \frac{8}{10} \)

3. \( \frac{7}{100} \) to Decimal:
- \( \frac{7}{100} = 0.07 \)

4. Decimal \( 0.75 \) to Fraction:
- \( 0.75 = \frac{75}{100} \)

---

Final Answers:

#### Part 1: Shaded Grids
1. \( \frac{10}{100} = 0.10 \)
2. \( \frac{30}{100} = 0.30 \)
3. \( \frac{89}{100} = 0.89 \)
4. \( \frac{5}{100} = 0.05 \)
5. \( \frac{100}{100} = 1.00 \)
6. \( \frac{1}{100} = 0.01 \)

#### Part 2: Conversions
1. \( \frac{4}{10} = 0.4 \)
2. \( \frac{8}{10} = 0.8 \)
3. \( \frac{7}{100} = 0.07 \)
4. \( \frac{75}{100} = 0.75 \)

---

Boxed Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{10}{100} = 0.10 & \frac{30}{100} = 0.30 & \frac{89}{100} = 0.89 \\
\frac{5}{100} = 0.05 & \frac{100}{100} = 1.00 & \frac{1}{100} = 0.01 \\
\frac{4}{10} = 0.4 & \frac{8}{10} = 0.8 & \frac{7}{100} = 0.07 & \frac{75}{100} = 0.75
\end{array}
}
\]