Introductory Chemistry Dr. George Lessard

Handling Numbers and Units Chapter 2 Chemistry 101 Lecture 2 Dr. George Lessard

Since Chemistry deals with matter, chemists measure Everybody thinks the more decimals the better Think about global warming Is it really getting warmer? And does it make a difference?

Atoms are very small, The Universe is very big Chemistry needs to measure very small numbers and very big numbers! How many zeros can you remember?

Exponents are one way of not having to count zeros Any number can be expressed as the product of a natural number and and exponent 300 = 3 x 102 N x (base 10)x

Any number, big and complex Look at the number, remember it can be broken down into pennies, dimes and dollars, how many dollars, how many dimes and how many pennies

Or small and simple Take the number. Move the decimal If moving the decimal makes the natural number smaller then the exponent must get bigger to make the number the same If moving the decimal makes the natural number bigger then the exponent must get smaller to make the number the same

There are many ways of expressing exponents, but! Scientists only use one method - SCIENTIFIC NOTATION In Scientific Notation there is only one number to the left of the decimal! Learn to use Scientific Notation

Skillbuilders Skillbuilder 2.1 Scientific Notation The total U.S national debt in 2010 was approximately $12,102,000,000,000. Express this number in scientific notation. Skillbuilder 2.2 Scientific Notation Express the number 0.000038 in scientific notation. 1Point Quiz- write it down without looking it up-1 minute Clinton lead Trump by thirteen million votes in the popular vote. Express it in scientific notation

But, still, how many zeros or how many digits? Depends! Depends on how precise the measurement Adding zeros does not add precision or accuracy In fact it may be misstating the precision-a lie! How many pennies? Not a problem! Seven?

But in Chemistry we cannot always be sure Sometimes it more than a Kilogram, but how much more? I can be sure that its over 45, but how far over? Remember the balance was made in China! That brings us to Significant Figures!

Significant Figures is a trick to save us having to think Any non-zero digit is significant It’s the zeros that have us confused What does a zero mean? All nonzero digits are significant Interior zeros are significant Trailing zeros after a decimal are significant

Some zeros only hold place they don’t define precision! These zeros are not significant, they do not define precision! Leading zeros are not significant Trailing zeros at the end of a number before a decimal point are not significant

Some numbers are exact-and have unlimited significant figures Direct counting of units =7 pennies Defined quantities-definitions =a meter Integral numbers in an = 1/2

Rounding off is related to significant figures How much does she weigh? Depends on why you are asking And it depends on how much she paid and how big the airplane is that she is flying on How much does she weigh?

You have known and estimated data To how many significant figures? 1 100 2 150 3 148 4 147.5 <5 round down >5 round up All are correct but a realistic value would be 150 For sure 14X Pretty sure 148 Estimated 147 .5

Scientific Notation allows correct significant figures 1 1x102 2 1.5 x 102 3 1.48 x 102 Learn how to use Scientific Notation

In problem solving always use the proper sig figs For addition and subtraction the rule is you can’t add value to garbage or subtract value from garbage

In multiplication and division you are limited by the least precise value Your answer can have no more significant figures than your least precise value

Skillbuilder 2.3 Reporting the Right Number of Digits Skillbuilders Skillbuilder 2.3 Reporting the Right Number of Digits A thermometer is used to measure the temperature of a backyard hot tub, and the reading is shown in Figure 2.4. Write the temperature reading to the correct number of digits. Skillbuilder 2.4 Determining the Number of Significant Figures in a Number How many significant figures are in each number? (a) 58.31 (b) 0.00250 (c) 2.7 × 103 (d) 1 cm = 0.01 m (e) 0.500 (f) 2100

Skillbuilders Skillbuilder 2.6 Significant Figures in Addition and Subtraction Perform the calculations to the correct number of significant figures. (a) 2.18 +5.621 +1.5870 –1.8 (b) 7.876 – 0.56 +123.792

Skillbuilders Skillbuilder 2.5 Significant Figures in Multiplication and Division Perform each calculation to the correct number of significant figures. (a) 1.10 x×0.512 x×1.301 x 0.005 ÷ 3.4 (b) 4.562 ×x 3.99870 ÷ 89.5