Units of Measurement

We measure everything!

see table 1.1 and 1.2

Examples of Measurements

will we use numbers that big/small in class?

yep! the mole

the mole

602,213,700,000,000,000,000,000 particles

or 6.022137 x 10 23 particles

scientific notation!

Scientific Notationa way to write really big

numbers

How to go to sci. notationNumbers bigger than ten will have

positive exponents that will equal how many times decimal moved to the left

36000 = 3.6 x 104

Numbers smaller than ten will have a negative exponents that will equal how many times it moved to the right

0.0081 = 8.1 x 10-3

Practice

Write in scientific notation1. 914 m2. 0.000 000 000 154 g

9.14 x 102 m

1.54 x 10-10g

How to go from sci. notation

Positive exponent = decimal moves to right8.25 X 104

= 82500

Negative exponent = decimal moves to left1.2 X 10 -3

= .0012

Practice

Write in scientific notation1. 2.157 X 10 5 L 2. 6.5 X 10-2 m

215 700 L .065 m

?’S

which measurement is best?

1.1200g

2.1.200 x 103g

3.1.2 x 103g

Significant Figures= digits recorded in measuring

the more sig figs the greater the certainty

Rules1. All nonzeroes are significant2. Zeroes in-between are significant3. Zeroes to the left are not significant4. Zeroes to the right are not significant

unless they follow a decimal.5. All numbers in scientific notation are

significant6. Exact numbers are obtained by

counting or definitions such as 1 in = 2.54 cm, and are considered infinite in significance

Practice

How many sig figs are in the following?1. 0.0950 m2. 9009.0 J3. 10 km4. 60 sec = 1min5. 5.50 x 108

ng

351infinite!3

so…which measurement is best?

1.1200g

2.1.200 x 103g

3.1.2 x 103g

Adding and Subtracting

Always use the least significant decimal place.

example: 1253.747 + 1.1 = 1254.81253.757 + 1.1= 1254.9 round up

.0365578 - .00223 =.03433 or 3.433 X 10-2

Practice

complete the following1. 8.7 g + 15.43 g + 19 g =2. 853.2 L - 627.443 L =3. 5.47 m + 11.0 m + 87.300 m =

43 g 225.8 L 103.8 m

Multiplying and DividingAll ways go by the least number

of significant figures.examples:

1253.747 X 1.1 =1379.1217 No

1400or 1.4 x 103

Practice

complete the following1. 4.32 cm x 1.7 cm =2. 38.742kg ÷ 0.421 =3. 5.40 m x 3.21 m x 1.871 m =

7.3 cm2

92.0 kg 32.4 m3

Combining the math

• Follow order of operations• 55.657 -55.654 X .033 = 4.54• 0.003 X .033 = 2 x 10-5 (1 sig fig) 4.54

Practice

8.52 + 4.1586 18.73 + 153.2 =

239.6 or

2.396 x 102

= 8.52 + 77.89 + 153.2 = 239.61 =