Aim: How to write in Scientific Notation and Count Significant FiguresDO NOW:

1.WHAT DOES 105 MEAN?

2.WHAT IS THE VALUE OF 105.

3.USING YOUR CALCULATOR, CALCULATE 4.5 X 106. (INPUT AS 4.5 X 10^6)

4.WOULD IT EASIER TO WRITE THE WHOLE VALUE OR JUST AS 4.5 X 106 EXPLAIN.

Scientific Notation

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

Scientific notation is the way that scientists easily handle very large numbers or very small numbers. For example, instead of writing 0.0000000056, we write 5.6 x 10-9

Examples

10000 = 1 x 104 24327 = 2.4327 x 104

1000 = 1 x 103 7354 = 7.354 x 103

100 = 1 x 102 482 = 4.82 x 102

10 = 1 x 101 89 = 8.9 x 101 (not usually done)

1 = 100

1/10 = 0.1 = 1 x 10-1 0.32 = 3.2 x 10-1 (not usually done)

1/100 = 0.01 = 1 x 10-2 0.053 = 5.3 x 10-2

1/1000 = 0.001 = 1 x 10-3 0.0078 = 7.8 x 10-3

1/10000 = 0.0001 = 1 x 10-4 0.00044 = 4.4 x 10-4

Writing in Scientific Notation

As you can see, the exponent of 10 is the number of places the decimal point must be shifted to give the number in long form. A positive exponent shows that the decimal point is shifted that number of places to the right. A negative exponent shows that the decimal point is shifted that number of places to the left.

Practice

Write out the whole number1.3 X 105

1.3 X 10 -5

Write the following in scientific notation0.000045613 450 000 000 000 000

Scientific Notation and Your Calculator

How to input scientific notation on your scientific calculator: Us the ^ button before exponent

( 3.7 x 10 ^ 3)

When doing calculations with scientific notation, put your numbers in scientific notation in parenthesis (2.3 x 104) – (3.7 x 103)

If a number like this shows up your calculator :

1.89E5 it is the same as 1.89 x 105

Your Turn (On your Own)

Question 1 Write in scientific notation: 0.000467 and 32000000

Question 2 Express 5.43 x 10-3 as a number not in scientific notation.

Question 3 (4.5 x 10-14) x (5.2 x 103) = ?Question 4 (6.1 x 105)/(1.2 x 10-3) = ?

Significant Figures

Significant figures refers the digits in a measured number (or in the result of a calculation with measured numbers) that include all certain digits plus a final digit having some uncertainty.

Rules to Significant Figures

All non-zero digits (1, 2, 3, 4, etc.) are significant. Zeroes between non-zero digits are significant. Ex: 101 Zeroes to the left of the first non-zero digit are not significant. Ex

0.0000101 Zeroes to the right of the last non-zero digit are significant if there is

a decimal point present, but not significant if there is no decimal point. Significant: 100. has three significant figures Not significant: 100 has one significant figure

Significant Figures in Calculations

For addition and subtraction problems, the answer should be rounded off to the same number of decimal places as the measurement with the fewest decimal places.

184.2 grams+ 2.324 grams = 186.524 grams ≈ 186.5 grams

Significant Figures in Calculations

For multiplication and division problems, round off the answer to the same number of significant figures in the measurement with the fewest significant figures.

100.0 grams of water x (0.0634 grams cisplatin/25.31 grams of water ) =

0.250493875 ≈ 0.250 grams