Questions: What is the area of a rectangular field that measures 29 yds by 37 yds? Write the result in units of yd^2 and round it to the correct number of significant figures. Use scientific notation in the form: xEm where x is a number with absolute value smaller than 10, and m is

What is the area of a rectangular field that measures 29 yds by 37 yds? Write the result in units of yd^2 and round it to the correct number of significant figures. Use scientific notation in the form: xEm where x is a number with absolute value smaller than 10, and m is

Transcript text: What is the area of a rectangular field that measures 29 yds by 37 yds? Write the result in units of $y d^{2}$ and round it to the correct number of significant figures. Use scientific notation in the form: xEm where $x$ is a number with absolute value smaller than 10 , and $m$ is

Solution

Solution Steps

Step 1: Calculate the area of the rectangle

The area $ A $ of a rectangle is given by the formula: \[ A = \text{length} \times \text{width} \] Substitute the given values: \[ A = 29 \, \text{yds} \times 37 \, \text{yds} \]

Step 2: Perform the multiplication

Multiply the two numbers: \[ A = 29 \times 37 = 1073 \, \text{yd}^2 \]

Step 3: Round to the correct number of significant figures

Both 29 and 37 have two significant figures. Therefore, the result should also be rounded to two significant figures: \[ A = 1.1 \times 10^3 \, \text{yd}^2 \]

Step 4: Write the result in scientific notation

Express the rounded result in scientific notation: \[ A = 1.1 \times 10^3 \, \text{yd}^2 \]