Description and exercises to take student through arithmetic and calculations needed for general chemistry.

1. General Chemistry
Numbers and
Calculations
Stephen Joseph Boylan 2016

2. 1. Significant figures and place of uncertainty. The significant figures are the digits that have
meaning in a number. The place of uncertainty is the digit at the right side of a number.
The digits that have meaning are called _______________________________ .
The digit at the right side is called ________________________________ .
2. Reading a digital display. Balance
A balance shows the above display for a volumetric flask.
2.1 Write the mass of the volumetric flask. ___________________
2.2 How many significant figures are there? ___________________
2.3 Write the digit of uncertainty. _____________________
A balance shows the above display for a volumetric flask.
2.4 Write the mass of the volumetric flask. ___________________
2.5 How many significant figures are there? ___________________
2.6 Write the digit of uncertainty. _____________________

3. A balance shows the above display for weighing paper..
2.7 Write the mass of the weighing paper. ___________________
2.8 How many significant figures are there? ___________________
2.9 Write the digit of uncertainty. _____________________
3. Reading an analog measurement. Graduated cylinder.
The graduated cylinder shown above contains water at the meniscus pointed by the arrow.
3.1 Write the volume of the water. ___________________
3.2 How many significant figures are there? ___________________
3.3 Write the digit of uncertainty. _____________________

4. The graduated cylinder shown above contains water at the meniscus pointed by the arrow.
3.4 Write the volume of the water. ___________________
3.5 How many significant figures are there? ___________________
3.6 Write the digit of uncertainty. _____________________
4. Reading an analog measurement. Thermometer.
4.1 Write the temperature shown on the thermometer. _______________
4.2 How many significant figures are there? ___________________
4.3 Write the digit of uncertainty. _____________________

5. 4.4 Write the temperature shown on the thermometer. _______________
4.5 How many significant figures are there? ___________________
4.6 Write the digit of uncertainty. _____________________
5. Exact number. Exact numbers specify the exact amount of an item of material. One five gallon
drum refers to exactly one drum at five gallons of material. Exact numbers do not have
significant figures. Exact numbers do not have a place of uncertainty. Exact numbers can be
spelled out.
Circle the exact numbers in the following instruction.
Place fifty milliliters of 0.12 M hydrochloric acid in a two hundred and fifty milliliter beaker.
Add 5.00 milliliters of 0.023 F sodium acetate.
6. Ambiguous numbers. A number is ambiguous when the numbers does not indicate the
numbers of significant figures. Ambiguous numbers have trailing zeros before a decimal point.
500 is an ambiguous number. Circle the ambiguous numbers.
600 45.2 0.0112 5300

6. 7. Scientific notation. Show ambiguous numbers in scientific notation.
One significant figure 5 x 102
Two significant figures 5.0 x 102
Three significant figures 5.00 x 102
How many significant figures are in 4.827 x 10-19 __________
8. Rounding up. If the digits to be discarded are greater than five, add one to the last digit of the
number.
8.1 Round the number 61.23468 to five significant figures. __________________
8.2 Round the number 152.873 to four significant figures. __________________
9. Rounding down. If the digits to be discarded are less than five, do not add to the last digit.
9.1 Round the number 95.4721 to four significant figures. ____________________
9.2 Round the number 5.4649 to three significant figures. ______________________
10. Rounding exactly five. If the digit to be discarded are exactly 5, round to an even number.
10.1 Round the number 95.475 to four significant figures. ____________________
10.2 Round the number 95.465 to four significant figures. ____________________
10.3 Round the number 95.475176 to four significant figures. ____________________
10.4 Round the number 95.46555 to four significant figures. ____________________
11. Adding numbers. Write the numbers in a column with the decimal point in a line. Add the
numbers. Round the sum to the number which has the least digits after the decimal point.
11.1 Add 35.124 and 127.1 ____________________________
11.2 Add 54.27 and 5.448 ________________________________
12. Subtracting numbers. Write the numbers in a column with the decimal point in a line.
Subtract the numbers. Round the result to the number which has the least digits after the decimal
point.
12.1 Subtract 53.124 from 581.1 ____________________________
12.2 Subtract 45.27 from 545.847 ______________________________
13 Multiplying numbers. Multiply the numbers. Round the answer to the number which has the
least number of significant figures.
13.1 Multiply 67.9 by 4.5 ____________________
13.2 Multiply 45 by 4.15 ____________________
14. Dividing numbers. Divide the numbers. Round the answer to the number which has the least
number of significant figures.

7. 14.1 Divide 45.6 by 23 ___________________________
14.2 Divide 189 by 4 ______________________________
15. Power of 10 to floating point.
103 equals 1000 10-6 equals 0.000001
3.4x103 equals 3400 6.59x 10-6 equals 0.00000659
15.1 Convert 8.394x109 to floating point _______________
15.2 Convert 2.114x10-3 to floating point _______________
16. Floating point to power of 10.
1000000 equals 106 0.000000001 equals 10-9
78900 equals 7.89x104 0.0000865 equals 8.65x10-5
16.1 Convert 561000 to power of 10 ______________________
16.2 Convert 0.000145 to power of 10 _____________________
17. Log base 10 to floating point
log 6.934 = 0.8409838… ~ 0.8410
17.1 Convert log base ten 4.587 to floating point __________________
17.2 Convert log base ten 12.5 to floating point __________________
18. Floating point to log base 10
101.23 = 16.982… ~ 17 10-4.35 = 4.466835922E-5 ~ 4.5 x 10-5
17.1 Convert 5.14 to log base 10 __________________
17.2 Convert 1.1 to log base 10 __________________
19. Natural logarithm to floating point
ln 5.84 = 1.764730797 ~ 1.8
19.1 Convert natural log 5.197 to floating point __________________
19.2 Convert natural log 4.625 to floating point __________________
20. Floating point to natural log.
e0.281 = 1.324453604 ~ 1.32
20.1 Convert 0.281 to natural log __________________
20.2 Convert – 0.541 to natural log __________________
21. Conversion factors. Prefixes.
kilo = k = 1000 = 103 centi = c = 0.01 = 10-2
Write the conversion factor to convert from kilojoules to joule. (kJ/J)

8. 22. Conversion factor. Units. 1 inch = 2.54 centimeters
Write the conversion factor to convert from inches to centimeters.
23. Reporting data average.
( 9.23 g/cm3 + 9.07 g/cm3 + 9.50 g/cm3 ) / 3 = 9.266666667 ~ 9.27 g/ cm3
Calculate the average of 7.89 g/cm3 8.01 g/cm3 and 7.64 g/cm3
average = __________________
24. Reporting data range. Calculate the range of 9.23 g/cm3 9.07 g/cm3 and 9.50 g/cm3
Range equals highest minus lowest = 9.50 g/cm3 - 9.07 g/cm3 = 0.430 g/ cm3
Calculate the range of 7.89 g/cm3 8.01 g/cm3 and 7.64 g/cm3
range = __________________
25. Multiplication and division These are the calculations that typically show up in test two.
408.3 nm * (10-9 m / 1 nm ) = 4.083 x 10-7 m
( 2.998 x 108 m/s ) / ( 4.083 x 10-7 m ) = 7.342 x 1014 1/s
7.342 x 1014 1/s x 6.626 x 10-34 j s = 4.865 x 10-19 joule per photon
25.1 Multiply 654.3 by 10-9 = ____________________
25.2 Divide 2.998 x 108 by 6.543 x 10-7 = ______________________
25.2 Multiply 4.582 x 1014 by 6.626 x 10-34 = _______________________
68.012g, 5, 2, 56.350g, 5, 0, 0.096g, 2, 6, 13.5mL, 3, 5, 18.4mL, 3, 4, 24.3C, 3, 3, 25.7C, 3, 7,
fifty, two hundred and fifty, 600, 5300, 4, 61.235, 152.9, 95.47, 5.46, 95.48, 95.46, 95.48, 95.47,
162.2, 59.72, 528.0, 500.58, 3.1x102, 1.9x102, 2.0, 5.x10, 8394000000, 0.002114, 5.61x105,
1.45x10-4, 0.6615, 1.10, 1.4x105