Page 320 - Theory and Problems of BEGINNING CHEMISTRY

APP.] SCIENTIFIC CALCULATIONS 309

A.35. Report the result for each of the following expressions to the proper number of significant digits:

−3
3
5 4
(a) (8.93 × 10 ) × (7.17 × 10 ) (d) (1.11 × 10 )
−7
2
−1
(b) (1.70 × 10 )/(3.85 × 10 ) (e) (−3.47 × 10 )(71.07)
−8
25
6
27
(c) (1.33 × 10 )/(1.69 × 10 ) ( f ) (2.00 × 10 ) − (2.00 × 10 )
Ans. (a) 64.0 (c) 7.87 × 10 13 (e) −2.47 × 10 1
(b)4.42 × 10 8 (d)1.52 × 10 20 ( f )1.98 × 10 27
A.36. Perform each of the following calculations, and report each answer to the proper number of significant
digits:
(a)6.24 × 2.000 ( f )31.5 + (−5.03)
(b)3.84/7.68 (g) −13 × (−13.9)
(c)8.14/29.13 (h)4.00 4
(d) (4.81) 2 (i) 13.8/(−71.7)
(e) (−1.15)(33.8) (j) 112.7 − (−66.473)
Ans. (a) 12.5 (c) 0.279 (e) −38.9 (g)1.8 × 10 2 (i) −0.192
(b) 0.500 (d) 23.1 ( f )26.5 (h) 256 (j) 179.2

A.37. To calculate 5.00 × 5.200, one student pressed the following keys:
5 . 0 0 × 5 . 2 0 0 =
Another student pressed the following keys:
5 × 5 . 2 =

Both students got the same display: 26. Explain why.
Ans. The calculator does not keep track of significant digits, so, for example, it does not differentiate between
5.00 and 5. The answer should be 26.0.

Supplementary Problems

A.38. Report the result for each of the following expressions to the proper number of significant digits:
7
2
(a)1.98 × 10 − 1.03 × 10 2 (c)5.54 × 10 + 6.76 × 10 2 ( f ) −2.445/41.052
1.59 × 10 16 (d)5.54 × 10 −7 + 6.76 × 10 −2 (g)17.0133 ÷ 17.0129
(b)
2
1.98 × 10 − 1.03 × 10 2
(e)4.184(125)(73.0 − 72.2)
Ans. (a)95 (d)6.76 × 10 −2 ( f ) −0.05956
(b)1.7 × 10 14 (e) 4 × 10 2 (g)1.00002
(c) 5.54 × 10 7

A.39. Solve for t:

15.1 years 17.4g
t = ln
0.693 12.1g
Ans. t = 7.92 years
2
x
A.40. State how you would obtain a value for the expression 2 , given that x = 3.
Ans. Exponentiation is done right to left. Thus, first square x, yielding 9, and then raise the 2 to the ninth power,
yielding 512.