Significant Figures and Scientific Notation



Significant Figures and Scientific Notation

Significant Figures – all the digits that can be known precisely in a measurement,

plus one digit that is estimated.

Why are significant figures important?

Indicates the precision of the measurement.

Rules for determining whether a digit is significant:

1. Every non zero digit in a reported measurement is significant

Example: 45.3 meters (3 significant figures)

2. Zeros appearing between nonzero digits are significant

Example: 30045 (5 significant figures)

3. Leftmost zeros appearing in front of nonzero digits are not significant

Example: 0.0071 (2 significant figures)

4. Zeros at the end of a number and to the right of a decimal point are

always significant

Example: 43.00 (4 significant figures)

5. Zeros at the rightmost end of a measurement that lie to the left of an

understood decimal point are not significant if they serve a placeholders to

show the magnitude of the number

Example: 8000 meters (1 significant figure)

6. There are 2 situations in which numbers have an unlimited number of

significant figures

1. Counting

Example: 23 people (Unlimited significant figures)

2. Involves exactly defined quantities such as those found within a

system of measurement

Example: 60 min = 1 hour

Determining significant figures when adding and subtraction

The answer to an addition or subtraction calculation should be rounded to the same number of decimal places as the measurement with least number of decimal places.

Example: Calculate the sum of the three measurements

12.52 meters + 349.0 meters + 8.24 meters

Since 349.0 has the fewest decimal places you answer must be rounded to one decimal place.

12.52 meters + 349.0 meters + 8.24 meters = 369.8 meters

Determining Significant figures when multiplying or dividing

The answer to a multiplication or division calculation should be rounded to the same number of significant figures as the measurement with the least amount of significant figures.

Example: 7.55 meters x 0.34 meters

Since 0.34 has the fewest significant figures, your answer must only have 2 significant figures.

7.55 meters x 0.34 meters = 2.6 meters2

Scientific Notation – a given number is written as the product of two numbers: a coefficient and 10 raised to a power.

Example. 602,000,000,000,000,000,000,000 = 6.02 x 10-23

Avogadro’s Number = Number of representative particles

contained in one mole of a substance

Adding and subtraction using scientific notation:

To add or subtract numbers expressed in scientific notation the exponents must be the same. Once the exponents are the same you add or subtract the coefficients and keep the exponents the same.

Example: (8.0 x 102) + (5.4 x 103)

You must first change the exponents so they are the same. To do that, move the decimal one to the left on the quantity 8.0 x 102 so the quantity is now

0.80 x 103. Now add the coefficients together and keep the exponents

(.80 x 103) + (5.4 x 103) = 6.2 x 103

Multiplication and Division using scientific notation:

To multiply or divide numbers expressed in scientific notation you multiply the coefficients and add the exponents, or divide the coefficients and subtract the exponents.

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

Example: (4 x 105)/(2 x 102) = 2 x 103

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download