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 (out of 100).
2. Converting between fractions and decimals.

Let's solve each part step by step.

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Part 1: Interpreting Shaded Grids

Each grid is divided into 100 smaller squares (10 rows and 10 columns). The number of shaded squares represents the numerator of a fraction with a denominator of 100. We need to count the shaded squares in each grid.

#### Grid 1 (Top Left):
- The grid has 10 shaded squares.
- Fraction: \( \frac{10}{100} \).

#### Grid 2 (Top Middle):
- The grid has 30 shaded squares.
- Fraction: \( \frac{30}{100} \).

#### Grid 3 (Top Right):
- The grid has 85 shaded squares.
- Fraction: \( \frac{85}{100} \).

#### Grid 4 (Middle Left):
- The grid has 10 shaded squares.
- Fraction: \( \frac{10}{100} \).

#### Grid 5 (Middle Middle):
- The grid has 100 shaded squares.
- Fraction: \( \frac{100}{100} \).

#### Grid 6 (Middle Right):
- The grid has 1 shaded square.
- Fraction: \( \frac{1}{100} \).

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Part 2: Converting Between Fractions and Decimals

#### Conversion Rules:
1. To convert a fraction to a decimal, divide the numerator by the denominator.
2. To convert a decimal to a fraction, express the decimal as a fraction with a denominator of 10, 100, etc., and simplify if possible.

#### Problem 1: \( \frac{4}{10} \)
- Divide 4 by 10: \( 4 \div 10 = 0.4 \).
- Decimal: \( 0.4 \).

#### Problem 2: \( \frac{\square}{10} = 0.8 \)
- To find the numerator, multiply 0.8 by 10: \( 0.8 \times 10 = 8 \).
- Numerator: \( 8 \).

#### Problem 3: \( \frac{7}{100} \)
- Divide 7 by 100: \( 7 \div 100 = 0.07 \).
- Decimal: \( 0.07 \).

#### Problem 4: \( \frac{\square}{100} = 0.75 \)
- To find the numerator, multiply 0.75 by 100: \( 0.75 \times 100 = 75 \).
- Numerator: \( 75 \).

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Final Answers:

#### Part 1: Shaded Grids
1. \( \frac{10}{100} \)
2. \( \frac{30}{100} \)
3. \( \frac{85}{100} \)
4. \( \frac{10}{100} \)
5. \( \frac{100}{100} \)
6. \( \frac{1}{100} \)

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

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Boxed Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{10}{100} & \frac{30}{100} & \frac{85}{100} \\
\frac{10}{100} & \frac{100}{100} & \frac{1}{100} \\
\frac{4}{10} = 0.4 & \frac{8}{10} = 0.8 & \frac{7}{100} = 0.07 & \frac{75}{100} = 0.75
\end{array}
}
\]