Prefixes and Symbols

Chem 1A

Chapter 1 Exercises

PREFIXES AND SYMBOLS

SI Prefixes you need to know by heart

PrefixSymbolPower of 10Decimal Representation

GigaG1091,000,000,000

MegaM1061,000,000

kilok1031,000

decid10-10.1

centic10-20.01

millim10-30.001

micro10-60.000,001

nanon10-90.000,000,001

picop10-120.000,000,000,001

Exponential notation:

104 = 10 x 10 x 10 x 10;10–4 = = = 0.0001

Conversion of decimal numbers to standard scientific notations and vice versa (examples):

12300 = 1.23 x 104 (trailing zeros are not significant; they are omitted in scientific notation.)

0.0012300 = 1.2300 x 10–3 (trailing zeros are significant; they cannot be omitted.)

9.2 x 104 = 92,000 (number must not contain decimal point);

2.90 x 10–3 = 0.00290

(Trailing zeros in scientific notations and numbers containing decimal points are always significant.)

Exercises #1:

1.Determine the number of significant figures in each of the following quantities.

(a) 0.00239 ______(b) 0.01950______(c) 1.07 x 10–3______

(d) 1.0040______(e) 48,000______(f) 0.082059______

(g) 93.00______(h) 3.00 x 108______(i) 100.______

2.Re-write the following decimal numbers in scientific notation.

(a) 0.000548580 = ______(b) 48,000 = ______

Exercise #1:

3.Re-write the following exponential numbers in the decimal forms.

(a) 3.982 x 105 = ______(b) 5.480 x 10–3 = ______

4.Round off the following quantities to the number of significant figures indicated in parenthesis.

(a) 0.037421 (3) = ______(b) 1.5587 (2) = ______

5.Express the following quantities using the significant figures that are consistent with the precision (that would imply the state error).

(a) 2.3 ± 0.001 = ______(b) 22,500 ± 10 = ______

6.Perform each of the indicated operations and report the answer to the proper number of significant figures.

(a) 32.27 x 1.54 ÷ 0.07925 = ______

(b) 8.2198 + 0.253 – 5.32 = ______

(d) 6.75 x 10-4 - 5.4 x 10-3 + 0.01953 = ______

(e) = ______(give appropriate unit)

Exercises #2:

Units Conversion

1.What are the SI units for the following measurements? Write the names and abbreviations.

Mass = ______;length = ______

Volume = ______;temperature = ______

Density = ______;Time = ______

______

Value Placement

Large UnitsNormalSmall Unitsvery small Units

Kilogram (kg)Gram (g)milligram (mg)microgram (g)

1,000 (103) g 1 g0.001 (10-3) g0.000,001 (10-6) g

Kilometer (km)Meter (m)millimeternanometer (m)

1,000 (103) m 1 m0.001 (10-3) m0.000,000,001 (10-9) m

Unit Conversion and value equivalences:

(a) Conversion of a large unit to smaller units, the numerical values get larger:

1 km = 103 m = 105 cm = 106 mm = 109m = 1012 nm

(b) Conversion of a small unit to larger units, the numerical values get smaller:

1 g = 10-3 mg = 10-6 g = 10–9 kg

2.English Units: fill in the following blank spaces with appropriate values:

1 mile = ______yards; 1 yard = ______feet; 1 foot = ______inches;

1 ton = ______pound (lb);1 lb = ______ounce (oz);

3.Perform the following conversion of units:

(a) Given: 1 yard = 36 inches;1 inch = 2.54 cm (exactly), and 1 m = 100 cm.

Convert 110. yards to meters and express your answer to three significant figures.

(b) Given: 1 mile = 1760 yd, 1 yard = 0.9144 m, and 1 km = 1000 m.

Convert 55 miles to kilometers and express your answer to two significant figures.

4.(a) Given: 1 lb = 16 oz.;1 kg = 2.205 lb, and 1 kg = 1000 g,

(i) Convert 5.0 pounds (lb) to kilograms and express your answer in two (2) significant figures.

(ii) Convert 25.0 ounces (oz) to grams and express your answer to three (3) significant figures.

(b) Given: 1 m = 100 cm, 1 cm3 = 1 mL, and 1 L = 1000 mL,

(i) Convert 25 m2 to cm2 and express your answer in two (2) significant figures.

(i) Convert 4.5 m3 to cm3 and then to liters. Express each answer in two significant figures.

(i) Convert 1 in2 to cm2 and 1 in3 to cm3. Express each answer in three (3) significant figures.

1 in2 = ?______cm2;1 in3 = ? ______cm3;

(ii) Convert 1 ft2 to m2 and 1 ft3 to m3. Express each answer in three (3) significant figures.

1 ft2 = ?______m2;1 ft3 = ?______m3.

5.Given that 1 mile = 1.609 km and 1 gallon = 3.7854 L, express 25 miles per gallon (mpg) to kilometers per liter (kmpL).

6.Given that 1 mile = 1.609 km; 1 km = 1000 m, and 1 hour = 3600 s, what is 3.00 x 108 m/s in miles per hour (mph)?

Statistical Analysis

Mean, Median, and Standard Deviation

Suppose that you obtain a sample of 10 pennies, weigh them individually, and the following masses in grams were collected:

2.50, 2.49, 2.52, 2.51, 2.51, 2.50, 2.52, 2.50, 3.01, and 2.51 g

Note that, while most of the pennies weigh about 2.5 g, one of them weighs 3.01 g, which is significantly different from the rest of the pennies. This penny does not belong to the group and should not be included in the statistical analysis. Subsequently, the mean, median, and standard deviation should be derived from the remaining 9 pennies. The data may be tabulated as shown in the following table.

Penny # / Mass, g / (Xi - ) / (Xi - )2
1 / 2.50 / -0.01 / 0.0001
2 / 2.49 / -0.02 / 0.0004
3 / 2.52 / 0.01 / 0.0001
4 / 2.51 / 0.00 / 0.0000
5 / 2.51 / 0.00 / 0.0000
6 / 2.50 / -0.01 / 0.0001
7 / 2.52 / 0.01 / 0.0001
8 / 2.50 / -0.01 / 0.0001
9 / 2.51 / 0.00 / 0.0000
Sum = / 22.56 / 0.07 / 0.0009

Mean = = = 2.507 g

The standard deviation: S = = = 0.01

Then, the mean will be re-written as 2.51 ± 0.01 g

Note that, standard deviation should have ONE significant figure only, because it represents the uncertainty in the data. Since this uncertainty appears on the second decimal digit, the calculated mean must be rounded off to 2.51 to be consistent with the precision of the data

To obtain the median value, the masses may be re-arranged in order of increasing values, in which the middle one will be the median value.

2.49, 2.50, 2.50, 2.50, 2.51, 2.51, 2.51, 2.52, 2.52

In the given data, the median value is 2.51 g (the same as the mean, which is not always the case).

Exercises #3:

1.The masses of three pennies obtained on three balances with different precision are as follows: 2.51 g, 2.508 g, and 2.5078 g. (a) What is the total mass of the three pennies expressed in correct significant figures? (b) Calculate the average mass of pennies.

2.A cylindrical solid metal measures 6.50 ± 0.02 cm long and 1.64 ± 0.02 cm in diameter and weighs 37.05 ± 0.01 g. Determine the volume and density of the metal and indicate the precision on each value.

3.Three students use different balances to weigh the same sample of copper shots three times and obtain the following results:

Weighing Trials / Student 1 / Student 2 / Student 3
1 / 16.015 g / 15.414 g / 14.893 g
2 / 16.002 g / 15.430 g / 14.902 g
3 / 15.980 g / 15.450 g / 14.896 g

(a) Calculate the average mass of the sample as determined by each student.

(b) Which sets of measurements are the most precise and the least precise?

(d) What type of error might have caused such differences in the mass of the sample?

Temperature:

4.Perform the following temperature conversions:

(a) 104oF to degrees Celsius and Kelvin, respectively.

(b) 158 K to degrees Celsius and Fahrenheit, respectively.

2.A T-scale thermometer is calibrated by setting the freezing point of water to –20oT and the boiling point of water to 230oT. Express the temperature 92.5oT in degrees Celsius and in Fahrenheit, respectively?

Exercise #4

Density:

1.A cylindrical metal bar is 8.50 cm long and has a diameter of 2.10 cm. If the mass of metal is 79.38 g, what is the density of metal?

2.A rectangular metal bar has the following dimension: 36.0 cm long, 10.0 cm wide, and 6.00 cm thick. Calculate the mass of the metal bar if it is made of: (a) pure lead (density = 11.35 g/cm3);

(b) pure gold (density = 19.3 g/cm3).

3.The mass of an empty flask is 64.25 g. When filled with water, the combined mass of flask and water is 91.75 g. However, when the flask is filled with an alcohol sample the combined mass is found to be 85.90 g. If we assume that the density of water is 1.00 g/mL, what is the density of the alcohol sample?

4.A rectangular copper sheet of uniform thickness measures 12.0 in. by 9.0 in. and weighs 936.0 grams. If the density of copper is 8.96 g/cm3, calculate the thickness of the sheet in millimeter.

5.An aluminum rod with a uniform diameter is 1.52 m long and weighs 1.05 kg. if the density of aluminum is 2.70 g/cm3, calculate the diameter of the rod.