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

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

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...

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

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

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

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?

● 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 g ● The digital scale is more accurate and will have more significant figures. When to use Significant figures

● 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

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

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.  kg  4th Exception: decimal points make all zeroes to the left significant.  m Has 4 sig figs Has 6 sig figs Has 5 sig figs

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

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

,000,050, How many sig figs?

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

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

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

 1.0cm x 4cm =  4.00cm x 18cm =  m ÷ 100.0sec =  708g ÷ 8.1L =  kg kg =  84m/s x s =  4cm²  72cm²  72.34m/sec  87.4g/L  kg  2600 m Sample Problems