1. Problem Solving Unit 1B Significant Figures, Scientific Notation & Dimensional Analysis

2. Significant Figures WWWWhat time is it? 1111:30 1111:28 1111:28:28 IIIIt depends on the situation

3. Significant Figures  In science, we describe a value as having a certain number of significant figures or digits. –Includes all the #’s that are certain and 1 uncertain digit. –1:30 has 2, 1:28 has 3, and 1:28:28 has 5 –There are rules that dictate which #’s are considered significant!

4. Rules for Significant Figures  Any non-zero # is considered significant  Zeroes! –Any zeroes between 2 numbers is significant  Ex. 205 has 3 sig. figs.  Ex. 4060033 has 7 sig. figs.  Ex. 10.007 has 5 sig. figs. –Any zeroes before a number are NOT significant  Ex. 0.054 has 2 sig. figs.  Ex. 0.000 005 has 1 sig. fig.

5. Rules for Significant Figures  Zeroes! Continued –Any zeroes after numbers may or may not be significant.  If there is a decimal point in the number, then YES, they are significant! –Ex. 12.000 has 5 sig. figs. –Ex. 0.1200 has 4 sig. figs. –Ex. 530.0000 has 7 sig. figs.  If there is no decimal point in the number, then NO, they aren’t significant! –Ex. 120 has 2 sig. figs. –Ex. 430 000 000 000 has 2 sig. figs.

6. Adding/ Subtracting and Significant Figures  The rule –When adding or subtracting the only significant figures you worry about are those after the decimal point. Your answer can have the same number of significant figures AFTER the decimal point as the original number that has the LEAST number of significant figures after the decimal point.

7. Examples  17.34 + 4.900 + 23.1 = 45.34 (1 sig. fig after decimal) = 45.3  9.80 – 4.782 = 5.318 (2 sig. figs. After decimal) = 5.32

8. Multiplying/ Dividing and Significant Figures  The rule –When multiplying or dividing, your answer must have the same number of significant figures as the original number that has the least number of significant figures total, not just after the decimal.

9. Examples  3.9 × 6.05 × 420 = 9909.9 (2 sig. figs total) = 9900 = 9.9 × 10 3 = 9.9 × 10 3  14.2 ÷ 5 = 2.82 (1 sig. fig total) = 3

10. Scientific Notation  Do you know this number? –300 000 000 m/s –It’s the speed of light.  Do you know this number? –0.000 000 000 752kg –It’s the mass of a dust particle.

11. Scientific Notation  Instead of counting zeroes and getting confused, we use scientific notation to write really big or small numbers. –3.00 × 10 8 m/s –7.53 × 10 -10 kg –The 1 st number is the COEFFICIENT- it is always a number between 1 and 10. –The 2 nd number is the BASE- it is the number 10 raised to a power, the power being the number of decimal places moved.

12. Using a calculator with scientific notation  A number written in scientific notation is NOT a math problem, it is a number in its own right. Therefore, there is a way to put the number into the calculator in order to add, subtract, multiply or divide.  IF you have a scientific calculator, find the button that says EE or EXP.

13. Scientific Calculators

14.  The EE or EXP button fills in for the × 10 part of the number written in scientific notation.  Let’s say you are adding these two numbers 3.21 × 10 7 + 6.99 × 10 6 = This is how you would enter it into your calculator 3.21 EE 7 + 6.99 EE 6 = And you would get your answer. 3.91 × 10 7

15. Dimensional Analysis  is a problem-solving method that uses the fact that any number or expression can be multiplied by one without changing its value. It is a useful technique. The only danger is that you may end up thinking that chemistry is simply a math problem - which it definitely is not.

16. Dimensional Analysis  Unit factors may be made from any two terms that describe the same or equivalent "amounts" of what we are interested in. For example, we know that  1 inch = 2.54 centimeters

17.  We can make two unit factors from this information:  Now, we can solve some problems. Set up each problem by writing down what you need to find with a question mark. Then set it equal to the information that you are given. The problem is solved by multiplying the given data and its units by the appropriate unit factors so that only the desired units are present at the end.

18.  (1) How many centimeters are in 6.00 inches?  (2) Express 24.0 cm in inches.

19.  You can also string many unit factors together.  (3) How many seconds are in 2.0 years?

20. Scientists generally work in metric units. Common prefixes used are the following:

21. Density- What is it?  Density is the ratio of mass to volume of a substance. –It can be used to identify a substance. –Ex. Water has a density of 1.00 g/mL –Ex. Gold has a density of 19.30 g/mL –Ex. Pumice has a density of 0.65 g/mL

22. Density & Temperature  Density = mass/ volume  d = m/V  Temperature = measure of the average kinetic energy a substance has –3 scales  Fahrenheit (°F)  Celsius (°C)  Kelvin (K)

23. Temperature Scale Conversions  From °C to °F –T °F = 1.8(T °C ) + 32°  From °F to °C –T °C =.56(T °F - 32°)  From °C to K –T = T + 273  From K to °C –T °C = T K - 273