Introductory Chemistry 101 Dr George Lessard Handling Numbers

Introductory Chemistry 101 Dr. George Lessard

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

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

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

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

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

Or small and simple F Take the number. Move the decimal F If moving the decimal makes the natural number smaller then the exponent must get bigger to make the number the same F 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! F Scientists only use one method - SCIENTIFIC NOTATION F In Scientific Notation there is only one number to the left of the decimal!

Skillbuilders Skillbuilder 2. 1 Scientific Notation The total U. S national debt in 2010 was approximately $12, 102, 000, 000. Express this number in scientific notation. Skillbuilder 2. 2 Scientific Notation Express the number 0. 000038 in scientific notation. 1 Point 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? How many pennies? Not a problem! Seven? F Depends! F Depends on how precise the measurement F Adding zeros does not add precision or accuracy F In fact it may be misstating the precision-a lie!

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

Significant Figures is a trick to save us having to think 1. All nonzero digits are significant 2. Interior zeros are significant 3. Trailing zeros after a decimal are significant FAny non-zero digit is significant FIt’s the zeros that have us confused FWhat does a zero mean?

Some zeros only hold place they don’t define precision! FThese zeros are not significant, they do not define precision! 4. Leading zeros are not significant 5. Trailing zeros at the end of a number before a decimal point are not significant

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

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

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

Scientific Notation allows correct significant figures F 1 F 2 F 3 1 x 102 1. 5 x 102 1. 48 x 102

In problem solving always use the proper sig figs FFor 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 FYour answer can have no more significant figures than your least precise value

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) (b) 2. 18 +5. 621 +1. 5870 – 1. 8 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