Chemistry Lecture L.S. 3

Significant Figuresand

Scientific Notation

Significant Figures

We use significant figures to demonstrate the uncertainty involved in a measurement. There are rules for determining the number of significant figures a measurement has.

Significant Figures

Non-zero integers always count as significant figures. Rules for zeros are as follows: Leading zeros are zeros that precede all the

non-zero digits. These are not significant. Captive zeros are those between non-zero

digits. These are significant. Trailing zeros are those at the right end of

the number. They are significant only if the digit contains a decimal.

Significant Figures

Exact numbers are those that are not obtained by using measuring devices. They are considered to have an infinite number of significant digits. An example of an exact number

would be a known constant used for calculations such as a conversion factor.

Significant Figures

Let’s try some counting! 1100

2 significant figures (trailing zeros w/ no decimal are not significant)

0.001 1 significant figure (leading zeros aren’t significant)

1.001 4 significant figures (captive zeros are always

significant) 1.100

4 significant figures (trailing zeros w/ decimal are significant)

Significant Figures

Questions?

Significant Figures

When doing calculations involving measurements, the answer must be presented with the correct number of significant figures. There are rules which dictate how many significant figures an answer should have based on the measurements used to calculate and the operations done.

Significant Figures

For multiplication and division, the number of significant figures in the result is the same as the number in the least precise measurement used in the calculation. 4.56 x 1.4 = 6.38 Since 1.4 is the least precise measurement,

the result should have 2 significant figures 4.56 x 1.4 = 6.4

Significant Figures

For addition and subtraction, the result has the same number of decimal places as the least precise measurement used in the calculation. 12.11 + 18.0 + 1.013 = 31.123 since 18.0 is the least precise

measurement, the result should only go out the tenths place.

12.11 + 18.0 + 1.013 = 31.1

Significant Figures

A Note on Rounding: If you are performing a series of

calculations, carry the extra digits through to the final result, then round.

If the digit to be removed is less than 5, the preceding digit stays the same. is greater than or equal to 5, the preceding digit

is increased by 1. Only look to the digit immediately following the

last significant digit for rounding purposes.

Significant Figures

Let’s try some! 97.382 + 4.2502 + 0.99195 102.614 (97.382 is least precise, so result should only go to

thousandths)

0.14 * 6.022 0.84 (0.14 is least precise, so result should only have 2

significant figures)

21.901 – 13.21 – 4.0215 4.67 (13.21 is least precise, so result should only go to

hundredths)

4.184 * 100.62 * (25.27 – 24.16) 467.3 (all but 100.62 have 4 significant figures, so result

should as well)

Significant Figures

Questions?

Scientific Notation

Scientific notation is used to make a very large or very small number easier to write. Scientific notation is also useful when trying to determine the number of significant figures as all non-significant digits are removed. Scientific notation expresses a number as a product of a number between 1 and 10 and the appropriate power of 10.

Scientific Notation

The distance from the Earth to the sun is approximately 93 million miles. 93,000,000 miles This number can be converted to scientific notation for ease of use. 93,000,000 = 9.3 * 10 * 10 * 10 * 10 * 10 * 10 * 10

93,000,000 = 9.3 * 107

Scientific Notation

The easiest way to determine the appropriate power of 10 for scientific notation is to count how many places the decimal will have to move in order to have a number between 1 and 10. When the decimal moves to the left the exponent is positive. When the decimal moves to the right the exponent is negative.

Scientific Notation

Scientific Notation

Let’s try some! 21,000 2.1 * 104

0.000256 2.56 * 10-4

10,010,000 1.001 * 107

0.000000080042 8.0042 * 10-8

Scientific Notation

When multiplying, only multiply the first part of each number. Then add the exponents together. If necessary, move the decimal to maintain scientific notation adjusting the exponent accordingly.

Scientific Notation

When dividing, only divide the first part of each number. The subtract the exponent belonging to the divisor from that of the divided. If necessary, move the decimal to maintain scientific notation adjusting the exponent accordingly.

Scientific Notation

To add or subtract in scientific notation, you must first make sure that the exponents are all the same. If the exponents are the same, then the first part of each number can be added or subtracted. If the exponents are not the same, then the numbers must be either taken out of scientific notation or manipulated so that the exponents do match.

Scientific Notation

Let’s try some! (4.32 * 104)(2.76 * 10-2) (4.32 * 2.76) * 104 + (-2)

11.9 * 102 1.19 * 103

(6.02 * 1023)/(2.2 * 103) (6.02/2.2) * 1023 – 3

2.7 * 1020

(3.25 * 105) + (4.2 * 104) (32.5 * 104) + (4.2 * 104) 36.7 * 104

3.67 * 105

Scientific Notation

Questions?

Assignment:

WS_SignificantFigures