Question

1. significant figures – measure the three diagrams and record measurements(length and width) to the correct number of significant figures examples:

Explanation:

To solve this problem, we need to measure the length and width of each diagram (rectangle) using a ruler and record the measurements to the correct number of significant figures. Here's a step - by - step guide:

Step 1: Gather the necessary tool

Get a ruler with appropriate precision (e.g., a centimeter ruler with millimeter markings). The precision of the ruler will determine the number of significant figures in our measurements. For a ruler with millimeter markings, we can measure to the nearest millimeter, and if we estimate, we can have one more significant figure.

Step 2: Measure the first rectangle

• Length measurement: Place the ruler along the length of the first rectangle. Align the zero mark of the ruler with one end of the length. Read the value at the other end. Let's assume we measure the length as \( l_1 = 3.5\space cm \) (here, 3 is a certain digit and 5 is an estimated digit, so it has two significant figures).
• Width measurement: Place the ruler along the width of the first rectangle. Align the zero mark of the ruler with one end of the width. Read the value at the other end. Let's assume we measure the width as \( w_1 = 1.2\space cm \) (two significant figures).

Step 3: Measure the second rectangle

• Length measurement: Follow the same process as for the first rectangle. Let's say the length \( l_2 = 4.8\space cm \) (two significant figures).
• Width measurement: Measure the width. Let's assume \( w_2 = 0.5\space cm \) (one significant figure, but if our ruler allows more precision, it could be \( 0.50\space cm \) with two significant figures).

Step 4: Measure the third rectangle

• Length measurement: Measure the length. Let's assume \( l_3 = 6.0\space cm \) (two significant figures, the zero here is a significant figure as it indicates the precision of the measurement).
• Width measurement: Measure the width. Let's assume \( w_3 = 0.8\space cm \) (one or two significant figures depending on the ruler's precision).

Please note that the actual measurements will depend on the size of the rectangles in the diagram and the precision of the measuring tool used. If you are using a digital caliper or a more precise ruler, the number of significant figures can be higher.

For example, if we use a ruler with millimeter markings (precision of \( 0.1\space cm \)):

• First rectangle: Length = \( 3.5\space cm \) (two significant figures), Width = \( 1.2\space cm \) (two significant figures)
• Second rectangle: Length = \( 4.8\space cm \) (two significant figures), Width = \( 0.50\space cm \) (two significant figures)
• Third rectangle: Length = \( 6.0\space cm \) (two significant figures), Width = \( 0.80\space cm \) (two significant figures)

If you want to calculate the area of each rectangle (using \( A = l\times w \)):

• Area of first rectangle: \( A_1=l_1\times w_1 = 3.5\space cm\times1.2\space cm = 4.2\space cm^2 \) (two significant figures)
• Area of second rectangle: \( A_2 = l_2\times w_2=4.8\space cm\times0.50\space cm = 2.4\space cm^2 \) (two significant figures)
• Area of third rectangle: \( A_3=l_3\times w_3 = 6.0\space cm\times0.80\space cm = 4.8\space cm^2 \) (two significant figures)

The key is to make sure that when measuring, you record all the certain digits plus one estimated digit (to determine the number of significant figures) and when performing calculations, you follow the rules for significant figures in multiplication/division (the result has the same number of significant figures as the least precise measurement).

Answer:

To solve this problem, we need to measure the length and width of each diagram (rectangle) using a ruler and record the measurements to the correct number of significant figures. Here's a step - by - step guide:

Step 1: Gather the necessary tool

Get a ruler with appropriate precision (e.g., a centimeter ruler with millimeter markings). The precision of the ruler will determine the number of significant figures in our measurements. For a ruler with millimeter markings, we can measure to the nearest millimeter, and if we estimate, we can have one more significant figure.

Step 2: Measure the first rectangle

• Length measurement: Place the ruler along the length of the first rectangle. Align the zero mark of the ruler with one end of the length. Read the value at the other end. Let's assume we measure the length as \( l_1 = 3.5\space cm \) (here, 3 is a certain digit and 5 is an estimated digit, so it has two significant figures).
• Width measurement: Place the ruler along the width of the first rectangle. Align the zero mark of the ruler with one end of the width. Read the value at the other end. Let's assume we measure the width as \( w_1 = 1.2\space cm \) (two significant figures).

Step 3: Measure the second rectangle

• Length measurement: Follow the same process as for the first rectangle. Let's say the length \( l_2 = 4.8\space cm \) (two significant figures).
• Width measurement: Measure the width. Let's assume \( w_2 = 0.5\space cm \) (one significant figure, but if our ruler allows more precision, it could be \( 0.50\space cm \) with two significant figures).

Step 4: Measure the third rectangle

• Length measurement: Measure the length. Let's assume \( l_3 = 6.0\space cm \) (two significant figures, the zero here is a significant figure as it indicates the precision of the measurement).
• Width measurement: Measure the width. Let's assume \( w_3 = 0.8\space cm \) (one or two significant figures depending on the ruler's precision).

Please note that the actual measurements will depend on the size of the rectangles in the diagram and the precision of the measuring tool used. If you are using a digital caliper or a more precise ruler, the number of significant figures can be higher.

For example, if we use a ruler with millimeter markings (precision of \( 0.1\space cm \)):

• First rectangle: Length = \( 3.5\space cm \) (two significant figures), Width = \( 1.2\space cm \) (two significant figures)
• Second rectangle: Length = \( 4.8\space cm \) (two significant figures), Width = \( 0.50\space cm \) (two significant figures)
• Third rectangle: Length = \( 6.0\space cm \) (two significant figures), Width = \( 0.80\space cm \) (two significant figures)

If you want to calculate the area of each rectangle (using \( A = l\times w \)):

• Area of first rectangle: \( A_1=l_1\times w_1 = 3.5\space cm\times1.2\space cm = 4.2\space cm^2 \) (two significant figures)
• Area of second rectangle: \( A_2 = l_2\times w_2=4.8\space cm\times0.50\space cm = 2.4\space cm^2 \) (two significant figures)
• Area of third rectangle: \( A_3=l_3\times w_3 = 6.0\space cm\times0.80\space cm = 4.8\space cm^2 \) (two significant figures)

The key is to make sure that when measuring, you record all the certain digits plus one estimated digit (to determine the number of significant figures) and when performing calculations, you follow the rules for significant figures in multiplication/division (the result has the same number of significant figures as the least precise measurement).