Page 315 - Theory and Problems of BEGINNING CHEMISTRY

304 SCIENTIFIC CALCULATIONS [APP.

Ans. (a)1
(b) The expression cannot be simplified.
(c) T 2 = 6T 1

3
3
A.4. What is the difference between (5.0 cm ) and (5.0 cm) ?
Ans. The exponent 3 outside the parentheses indicates that the 5.0 is to be cubed, as well as the unit centimeter.
The exponent inside the parentheses acts on the unit only.

A.5. In each of the following sets, are the expressions equal?

1 a a a a a 1

(a) a (c) + +
b + c b + c b + c b c b c
a 1 a a 1
(b) × ×
bc b c b c
Ans. (a) Both expressions are equal.
(b) All three expressions are equal.
(c) None of the expressions is equal to any of the others.

A.6. Are the following expressions equal to each other?
(a) a(b + c) − d(e − f ) ab + ac − de − df
(b) (a + b)(c − d) − (e + f )(g − h) ac + bc − ad − bd − eg + eh − fg + fh
Ans. (a) They are not equal: −d times − f is equal to + df, not −df.
(b) They are equal.

A.7. Evaluate each of the following pairs of expressions, using a = 4 and b = 3. In each case, determine if
the two expressions are equal.

1 1 1 1 1 1 1 1 1
(a) + (b) − (c) ×
a b a + b a b a − b a b ab
Ans. (a) Not equal: 0.583
= 0.143
(b) Not equal: −0.083
= 1
(c) Equal: 0.0833 = 0.0833

A.8. What is the unit of the price of gasoline?
Ans. Dollars/gallon or dollars/liter

A.9. What units are obtained when a mass in grams is divided by a volume in (a) milliliters (mL), (b) cubic
3
3
centimeters (cm ), and (c) cubic meters (m )?
Ans. (a) g/mL (b)g/cm 3 (c)g/m 3

A.10. What units are obtained when a volume in milliliters is divided into a mass in (a) kilograms, (b) grams,
and (c) milligrams?

Ans. (a) kg/mL (b) g/mL (c) mg/mL