1. Chemistry by the numbers Units of Measurement – The Metric System Length: Mass: Volume: Temperature: Pressure: milli-centi-deci-(unit)deka-hecta-kilo- 0.0010.010.11101001000 ________ meter ________ gram ________ liter _____ Celsius ____ atmosphere

2. Chemistry by the numbers ● What is the mass of an electron? 0.000,000,000,000,000,000,000,000,000,000,911 kg ● What is the distance between our sun and Pluto? 5,913,520,000,000 m ● Is there a better way to write these numbers? YES! Scientific Notation

3. Chemistry by the numbers ● First, locate the first significant digit Scientific Notation Move this decimal......to just after the first significant digit ● Then count the places the decimal moved...

4. Chemistry by the numbers ● Your new number is then written times 10 to the number of places you moved the decimal Scientific Notation ● The number is negative because the original number is a decimal So try it with the other number: 5,913,520,000,000 m → kg

5. Accuracy vs. Precision Accuracy: measurements that are close to the true value. Precision: measurements that are consistent.

7. Significant Figures ● 2 kinds of numbers: – Exact: The precise amount. – (ie Money in your pocket) – Approximate: Anything MEASURED. – No measurement is perfect

8. When to use Significant figures ● Scientists only use numbers that are reliable. Example: The mass of a coin on a triple-beam balance is 2.7g the mass of the same coin on a digital scale is 2.700g Are they the same number?

9. ● To a mathematician, yes. ● To a scientist, No! ● 2.700g to a scientist means the measurement is accurate to within one thousandth of a gram. 2.700g ● The digital scale is more accurate and will have more significant figures. When to use Significant figures

10. ● Rule 1: All numbers are significant starting with the first non-zero digit on the left. ● 1st Exception: In whole numbers that end in zero, the zeros at the end are not significant. How many sig figs? Has 4 sig figs Has 3 sig figs ??? Has 1 sig fig

11. How many sig figs?  7  40  0.5  0.00003  7 x 10 5  7,000,000 11 11 11 11 11 11

12. How do I know how many?  2nd Exception: Any zeroes between two non-zero numbers are significant.  2002 sec  3rd Exception: Zeroes to the right of a decimal are significant.  11.4000kg  4th Exception: decimal points make all zeroes to the left significant.  90100. m Has 4 sig figs Has 6 sig figs Has 5 sig figs

13. How do I know how many? Sig Figs & Scientific Notation Count all the numbers before the x10 9.3x10²cm = 4.1000x10³³kg = 2 5

14.  1.2  2100  56.76  4.00  0.0792  7,083,000,000 22 22 44 33 33 44 How many sig figs?

15. 3401 2100 2100.0 5.00 0.00412 8,000,050,000. 4 2 5 3 3 10 How many sig figs?

16. When Adding or subtracting measurements – Answer will have the same decimal place as the least accurate number – Ex: 2.45 cm + 1.2cm = 3.65cm? – 1.2cm is least accurate so… round to the one decimal 7.432L + 2L Sig Fig Calculations  3.7cm = 9.432L round to  9L

17. 123.0cm – 99.82cm = 2100.mL + 101mL = 88.772g – 17.1g = 24.00cm – 18cm = 7234.1m + 1000.0m = 708g – 8.4g = 23.2cm 2201mL 71.7g 6cm 8234.1m 700g Sample Problems

18. ● Multiplying or dividing, significant figures Answer will have the same sig. figs as the least reliable measurement. 56.780cm x 2.45cm = Sig Fig Calculations 5 sig figs 3 sig figs 139.111 cm 2 139.111 cm 2 → 139 cm 2 Round to 3 sig figs... If two numbers have the same reliability, use the least amount of sig figs. 12.00km x 1.01km = 12.12km 2 → 12.1km 2

19.  1.0cm x 4cm =  4.00cm x 18cm =  7234.1m ÷ 100.0sec =  708g ÷ 8.1L =  298.01kg + 34.112kg =  84m/s x 31.221s =  4cm²  72cm²  72.34m/sec  87.4g/L  332.12kg  2600 m Sample Problems