Question

the shaded parts of this diagram represent 0.10 or \10 hundredths.\ they also represent 0.1 or \1 tenth.\ numbers like 0.01, 0.10, and 0.1 are written in decimal notation. look at the shaded parts of each diagram in the first problem. write the numbers they represent in decimal notation. what number does the shaded parts of each diagram represent? write the number as a fraction and in decimal notation. (4) diagram ____ __ (5) diagram __ ____

Explanation:

To solve this, we analyze the diagrams (assuming each diagram is a grid of 10x10 = 100 small squares, as typical for decimal/fraction representation of hundredths).

For 4. (Assuming the first diagram set):

Step 1: Count shaded squares

Suppose the first diagram (left) is fully shaded (100 squares) and the second (right) has 40 shaded (since it’s a 10x10 grid, 4 rows or columns shaded). Wait, actually, let's assume standard 10x10 grids (total 100 parts, each 0.01 or $\frac{1}{100}$).

• If the first diagram is 1 whole (100/100) and the second is 0.4 (40/100), but maybe the first diagram is 1 (100/100) and the second is 0.4 (40/100), so total:

Fraction: $1 + \frac{40}{100} = \frac{140}{100} = \frac{7}{5}$ (simplified), Decimal: $1.4$

Wait, maybe the diagrams are two parts: left is a whole (10x10 shaded, so 1) and right is a 10x10 grid with 4 columns/rows shaded (40 squares). So:

Step 1: Identify each diagram’s value

• Left diagram: 10x10 shaded = $1$ (or $\frac{100}{100}$).
• Right diagram: 40 out of 100 shaded = $\frac{40}{100} = \frac{2}{5}$, or $0.4$.

Step 2: Combine (if it’s a sum)

Total fraction: $1 + \frac{40}{100} = \frac{140}{100} = \frac{7}{5}$ (or keep as $\frac{140}{100}$).
Total decimal: $1 + 0.4 = 1.4$.

For 5. (Second diagram set):

Suppose left is 1 (100/100) and right is 0.6 (60/100):

Step 1: Identify each diagram’s value

• Left: $1$ (100/100).
• Right: 60/100 = $\frac{3}{5}$, or $0.6$.

Step 2: Combine

Total fraction: $1 + \frac{60}{100} = \frac{160}{100} = \frac{8}{5}$, Decimal: $1 + 0.6 = 1.6$.

Final Answers (assuming typical 10x10 grids):

4.

Fraction: $\boldsymbol{\frac{140}{100}}$ (or $\frac{7}{5}$), Decimal: $\boldsymbol{1.4}$

5.

Fraction: $\boldsymbol{\frac{160}{100}}$ (or $\frac{8}{5}$), Decimal: $\boldsymbol{1.6}$

(Note: Exact values depend on the actual diagram shading, but this is a standard interpretation of 10x10 grids for decimals/fractions.)

Answer:

To solve this, we analyze the diagrams (assuming each diagram is a grid of 10x10 = 100 small squares, as typical for decimal/fraction representation of hundredths).

For 4. (Assuming the first diagram set):

Step 1: Count shaded squares

Suppose the first diagram (left) is fully shaded (100 squares) and the second (right) has 40 shaded (since it’s a 10x10 grid, 4 rows or columns shaded). Wait, actually, let's assume standard 10x10 grids (total 100 parts, each 0.01 or $\frac{1}{100}$).

• If the first diagram is 1 whole (100/100) and the second is 0.4 (40/100), but maybe the first diagram is 1 (100/100) and the second is 0.4 (40/100), so total:

Fraction: $1 + \frac{40}{100} = \frac{140}{100} = \frac{7}{5}$ (simplified), Decimal: $1.4$

Wait, maybe the diagrams are two parts: left is a whole (10x10 shaded, so 1) and right is a 10x10 grid with 4 columns/rows shaded (40 squares). So:

Step 1: Identify each diagram’s value

• Left diagram: 10x10 shaded = $1$ (or $\frac{100}{100}$).
• Right diagram: 40 out of 100 shaded = $\frac{40}{100} = \frac{2}{5}$, or $0.4$.

Step 2: Combine (if it’s a sum)

Total fraction: $1 + \frac{40}{100} = \frac{140}{100} = \frac{7}{5}$ (or keep as $\frac{140}{100}$).
Total decimal: $1 + 0.4 = 1.4$.

For 5. (Second diagram set):

Suppose left is 1 (100/100) and right is 0.6 (60/100):

Step 1: Identify each diagram’s value

• Left: $1$ (100/100).
• Right: 60/100 = $\frac{3}{5}$, or $0.6$.

Step 2: Combine

Total fraction: $1 + \frac{60}{100} = \frac{160}{100} = \frac{8}{5}$, Decimal: $1 + 0.6 = 1.6$.

Final Answers (assuming typical 10x10 grids):

4.

Fraction: $\boldsymbol{\frac{140}{100}}$ (or $\frac{7}{5}$), Decimal: $\boldsymbol{1.4}$

5.

Fraction: $\boldsymbol{\frac{160}{100}}$ (or $\frac{8}{5}$), Decimal: $\boldsymbol{1.6}$

(Note: Exact values depend on the actual diagram shading, but this is a standard interpretation of 10x10 grids for decimals/fractions.)