If computing N(t) = Pa^t where P=642.035376 and a = 2.900129566 (both are stored in calculator), to what extent should the values of N(5), N(7) and N(9) be rounded? and why?
Note:
N(5)= 131,718
N(7)= 1,107,849
N(9)= 9,317,847
Hmmmm. How many sig digits are in t? ONE? 5,7,9?
So the answer is ONE for because t only has one sig fit? instead of the 9 sig figs of P which I thought was the lowest?
To determine the extent to which the values of N(5), N(7), and N(9) should be rounded, we need to consider the level of precision provided by the values of P and a.
Given that P is given to six decimal places (642.035376) and a is given to nine decimal places (2.900129566), we should maintain the same level of precision in our calculations to ensure accurate results.
Therefore, we should round the values of N(5), N(7), and N(9) to the nearest whole number because the original values of P and a do not provide enough decimal places for a higher level of precision.
Rounding N(5):
N(5) = Pa^5 = 642.035376 * (2.900129566)^5 ≈ 131718.38315408948
Rounded to the nearest whole number: N(5) ≈ 131,718
Rounding N(7):
N(7) = Pa^7 = 642.035376 * (2.900129566)^7 ≈ 1107849.0153631826
Rounded to the nearest whole number: N(7) ≈ 1,107,849
Rounding N(9):
N(9) = Pa^9 = 642.035376 * (2.900129566)^9 ≈ 9317847.108367292
Rounded to the nearest whole number: N(9) ≈ 9,317,847
By rounding the values of N(5), N(7), and N(9) to the nearest whole number, we adhere to the level of precision provided by the original values of P and a.