Chemistry by the numbers

Units of Measurement – The Metric System

• Length:

• Mass:

• Volume:

• Temperature:

• Pressure:

milli- centi- deci- (unit) deka- hecta-

kilo-

0.001 0.01 0.1 1 10 100 1000

________ 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 digitScientific 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. PrecisionAccuracy: 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.

2.700g

●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 0.00003 7 x 105

7,000,000

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.

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

How do I know how many?Sig Figs & Scientific Notation

Count all the numbers before the x10

9.3x10²cm =

4.1000x10³³kg =

25

1.2 2100 56.76 4.00 0.0792 7,083,000,000

2 2 4 3 3 4

How many sig figs?

340121002100.05.000.004128,000,050,000.

4253310

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 = 88.772g – 17.1g =24.00cm – 18cm =7234.1m + 1000.0m =708g – 8.4g =

23.2cm2201mL71.7g6cm8234.1m700g

Sample Problems

●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 cm2

139.111 cm2 → 139 cm2

Round to 3 sig figs...

If two numbers have the same reliability, use the least amount of sig figs.

12.00km x 1.01km = 12.12km2 → 12.1km2

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