ChemistryWilbraham

StaleyMatta

Waterman

Chapter 3: Scientific Measurement

Copyright © 2005 Pearson Education & Prentice-Hall, Inc.

Prompt:

When you make a measurement, what are some possible sources of uncertainty?

How do you write numbers in scientific notation?

Measurement: is a quantity that has both a number and a unit.

examples:

height (66 inches)

age (15)

body temperature (37oC).

a gram of hydrogen, for example= 602,000,000,000,000,000,000,000 hydrogen atoms.

The mass of an atom of gold = 0.000000000000000000000327 gram.

Work more easily with number by writing them in scientific notation.

scientific notation: a given number is written as the product of two numbers: a coefficient and 10 raised to a power.

For example, 602,000,000,000,000,000,000,000 can be written in scientific notation as 6.02 x 1023

The coefficient in this number is 6.02, the power of 10, or exponent, is 23.

In scientific notation, the coefficient is always a number greater than or equal to one or less than ten. The exponent is an integer.

Positive exponent: indicated how many times the coefficient must be multiplied by 10.

Negative exponent: indicated how many times the coefficient must be divide by 10.

Positive exponent!

the exponent must be divided by 10

6, 300,000 = 6.3 x 106

94,700 = 9.47 x 104

equals the number of places that the original decimal point has been moved to the left.

Larger than 10?

Less than 10

Negative Exponent!

0.000 008 = 8 x 10-6

0.0736 = 7.36 x 10-3

The value of the exponent equals the number of places the decimal has moved to the right.

Multiplication of numbers in scientific notation:

multiply the coefficients and add the exponents

(3 x 104) x (2 x 102) = (3x 2) x 104+2 = 6 x 106

(2.1 x 103) x (4.0 x 10-7) = (2.1 x 4) x 103+(-7) = 8.4 x 10-4

Multiplication

Division

To divide numbers written in scientific notation

divide the coefficient and subtract the exponent in the denominator from the exponent in the numerator.

(3 x 105) / (6.0 x 102) = (3.0 / 6.0) x 105-2 = 0.5 x 103 = 5.0 x 102

Addition and subtraction

if you are not using a calculator

then exponents must be the same.

(5.4 x 103) + (8.0 x 102) = first rewrite the second number so equation is a 3.

(5.4 x 103) + (8.0 x 102) = (5.4 x 103) + (0.80 x 103)

(5.4 + 0.08) x 103

= 6.2 x 103

Using Scientific Notation

Solve in your notes:

a. (8.0 x 10-2) x (7.0 x 10-5)=

b. (7.1 x 10-2) + (5 x 10-3)=

a. (8.0 x 10-2) x (7.0 x 10-5)= (8.0 x 7.0) x 10-2 (-5)= 56 x 10-7

= 5.6 x 10-6

b. (7.1 x 10-2) + (5 x 10-3)= (7.1 x 10-2) + (0.5 x 10-2)

= 7.6 x 10 -2

Accuracy, Precision and Error

How do you evaluate accuracy and precision?

In groups of 2-3 students, use a meter-stick and a metric ruler to measure the height of the:

wall

deck

front bench

to the nearest meter, centimeter, or millimeter.

Make a table for your data!

m cm mm

Wall

Deck

Bench

When finished:

Compare your results- Make a larger table on the white board, and write your findings in the appropriate locations.

Measurements can be correct but have degrees of uncertainty.

Were the measurements for each type of units the same?

Which unit provided the most accurate data?

Millimeters provides the closest measurement to the actual length.