Question

P = e f e = 4.8 correct to 2 significant figures. f = 0.26 correct to 2 significant figures. Work out the lower bound for the value of P . Give your answer correct to 3 significant figures. (2 marks)

Answer 1

To calculate the lower bound for P, multiply the lower bounds of e and f. The lower bound for e is 4.85, and for f it is 0.265. The product, rounded to three significant figures, is 1.29.

Step-by-step explanation:

To find the lower bound of P, we need to perform a multiplication using the lower bounds of e and f. Since e = 4.8 and f = 0.26 are both correct to two significant figures, their lower bounds are calculated as follows:

• For e, the next number with two significant figures after 4.8 is 4.9. Thus, the lower bound of e is halfway between 4.8 and 4.9, so it is 4.85.
• For f, the next number with two significant figures after 0.26 is 0.27. Therefore, the lower bound of f is halfway between 0.26 and 0.27, so it is 0.265.

Multiplying the lower bounds of e and f will give us the lower bound of P:

P (lower bound) = e (lower bound) × f (lower bound)
= 4.85 × 0.265 = 1.28525

When rounded to three significant figures, the lower bound for P is 1.29.

Answer 2

Step-by-step explanation:

P = efe =4.8

f =0.26

substitute the value of P and f into the equation to obtain the value of e

4.8 = e*0.26*e

4.8 = 0.26*e^2

make e^2 the subject of the formula

e^2 =4.8/0.26 =18.62

find the square root of e

e =
`√(x) 18.46\\`

e = 4.3

Lower bound of P = 4.8 - 4.79 = 0.01