Express (158 lb) 2 to three significant figures with appropriate units

Answer: 2.50 * 10⁴

Justification:

1) The expression is: (158 lbs) ²

2) When two amounts are multiplied, the product must be shown with the same number of significant figures of that of the factor with the least number of significant figures.

3) So you have to muliply 158 by itself (square) and then round to 3 significant figures.

4) The number 158 has 3 significan figures, so the product shall show also 3 significant figures:

(158 lb) ² = 158 lb * 158 lb = 24,964 lb², which must be rounded to 3 significant figures: 25,000.

Since, the fourth figure was greater than 5, the third signficant figure must be increased. Since the third signficant figure is 9, the increase is translated to the second significant figure.

5) Now, to indicate tha the number of significan figures is 3, you have to use scientific notation:

25,000 = 2.50 * 10³, where the 3 signficant figures are 2, 5, and 0.

(158lb) 2 = 158 lb * 158 lb

This gives us 24964 lb^2

To solve the solution to 3sf we obtain 25000 lb^2.

Hence 25000 to 3sf