To convert 3 square feet to square centimeters, multiply 3 by $9.29 \times 10^{-2}$
True
False
Answer (1)
Determine the conversion factor between square feet and square centimeters.
Calculate the square of 30.48 cm (since 1 foot = 30.48 cm) to find the number of square centimeters in a square foot.
Compare the calculated value (929.0304) with the given value ( 9.29 × 1 0 − 2 = 0.0929 ).
Since the values do not match, the statement is false. F a l se
Explanation
Analyze the problem Let's analyze the problem. We need to determine if multiplying 3 square feet by 9.29 × 1 0 − 2 converts it to square centimeters. This means we need to find the correct conversion factor between square feet and square centimeters and compare it with the given value.
Find the conversion factor First, we need to find the correct conversion factor. We know that 1 foot is equal to 30.48 centimeters. 1 foot = 30.48 cm Therefore, 1 square foot is equal to ( 30.48 ) 2 square centimeters. 1 ft 2 = ( 30.48 cm ) 2
Calculate the square Now, let's calculate ( 30.48 ) 2 :
( 30.48 ) 2 = 929.0304 So, 1 square foot is equal to 929.0304 square centimeters. 1 ft 2 = 929.0304 cm 2
Compare the values The problem states that to convert 3 square feet to square centimeters, we multiply 3 by 9.29 × 1 0 − 2 . This implies that 1 square foot is equal to 9.29 × 1 0 − 2 square centimeters. However, we found that 1 square foot is equal to 929.0304 square centimeters. Let's calculate 9.29 × 1 0 − 2 :
9.29 × 1 0 − 2 = 0.0929 This is not equal to 929.0304.
Conclusion Since 1 square foot is 929.0304 square centimeters, to convert 3 square feet to square centimeters, we should multiply 3 by 929.0304, not by 9.29 × 1 0 − 2 . Therefore, the statement is false.
Examples
When renovating a house, you might need to convert the area of a room from square feet to square centimeters to order tiles from a European manufacturer. Knowing the correct conversion factor ensures you order the right amount of material, avoiding shortages or excess. This conversion is also essential in architectural design, where precise measurements are critical for planning and construction.
