A. 322354.090, 322354.1, 322350, and 322400.
B. 1452 × 9076.7 = 13,179,368.4, which to 4 significant digit is 13,180,000.
C. 46,371 ÷ 0.00728 = 6,369,642.8571428571428..., which to 1 significant digits is 6,000,000.
D. The absolute error is 20 pounds – 18 pounds = 2 pounds, and the relative error is 2/18 or 11%.
E. The absolute error is 60 minutes – 65 minutes = -5 minutes, and the relative error is (-5 min)/(65 min) or 7.7%. That is, the person organizing the meeting underestimated how long the meeting would take by 7.7%. (However, one can make the case that the correct way to measure the relative error is the other way around; i.e., the meeting ran over by (+5 min)/(60 min) or 8.3%.)
F. The absolute error is 0.1 cm – 0.2 cm = -0.1 cm, and the relative error is (-0.1 cm)/(0.2 cm) = -50%. That is, the estimate of the diameter was too low by 50%. (However, in a case where there are products and standards, it is also customary to describe the error by saying how much reality deviates from what is desired; that is, we would say that the diameter of the ball-bearing is (+0.1 cm)/(0.1 cm) = 100% larger than specifications.)
G. Recall from the table at the bottom of page 169 that zeros to the right of the last nonzero digit but before the decimal point are not significant unless stated otherwise. Since we not told otherwise, we probably should assume that the number 50 has only one significant digit, not two. That is, it is only correct to within the nearest ten. So after we add 50 kg and 1.25 kg, obtaining 51.25 kg, we have to round to the nearest 10, obtaining 50 (not 51). However, the answer 51 will be accepted for full credit, since this is a gray area.
H. (630,000 constituents) × ($4.25 / constituent) = $2,677,500.00. Since 630,000 has 2 significant digits and 4.25 has 3 significant digits, we should report our answer to 2 significant digits as $2,700,000.
I. ($45,000) × (CPI2002 / CPI1981) = ($45,000) × (179.9 / 90.9) = $89059.4... , which to 2 significant digits is $89,000.
J. (CPI2002 – CPI2001)/CPI2001 = (179.9-177.1)/177.1 = 2.8/177.1 = 1.6% (note that we only keep two significant digits, since 8.8 has only two significant digits).
K.
($380,000) × (100/182) = $208,791;
that's $209,000 (to three significant digits)
or $210,000 (to two significant digits).
($380,000) × (495/182) = $1033516;
that $1,030,000 (to three significant digits)
or $1,000,000 (to two significant digits).
($380,000) × (52/182) = $108571;
that's $109,000 (to three significant digits)
or $110,000 (to two significant digits).
Note that in this case, the valuation of the house
is probably valid to only 2 or 3 significant digits,
so you shouldn't give more than 2 or 3 significant digits in your answer.
(But you won't lose points on this one if you do,
because in the real world, figures like $380,000 may start out as estimates,
but when they become prices all their digits become significant by fiat.)
L. The relative increase in airfare was ($310-$230)/($230) = 80/230 = 35% (note that there are only 2 significant digits, since 80 only has 2 significant digits), while the CPI went up by (179.9-82.4)/82.4 = 118%. So airfare went up slower than inflation.
M. The relative increase in the cost of college at a public university was ($9700-$2490)/($2490) = 7210/2490 = 290% (to three significant digits). So college costs went up faster than inflation.
N.
(a) As measured in terms of the (national average) buying power
of the 1980-1982 dollar,
the buying power of my annual salary for the Florida job is
$30,000 / 1.685 = $17804,
while the buying power of my annual salary for the New York job is
$40,000 / 2.127 = $18806.
Since the latter is greater,
the New York job will give me more spending-power.
(Alternative solution: If the Florida job pays $30,000,
a comparable salary for New York wouuld be
$30,000 × (CPINY/CPIFL) =
$30,000 × (212.7/168.5) = $37,869.
Since the New York job actually offers slightly more than this,
the New York job will give me more spending-power.)
(b)
The buying power of my annual salary for the Florida job
in 1980-1982 dollars is $50,000 / 1.685 = $29674
and the buying power of my annual salary for the New York job
in 1980-1982 dollars is $60,000 / 2.127 = $28209.
Since the former is greater,
the Florida job will give me more spending-power.