Scientific Notation

Scientific Notation• A number written as a product of two numbers:

a coefficient and a power of 10 • Designed for the expression of very big and

very small numbers– 3.6 x 104

– 1 gram of hydrogen contains 301,000,000,000,000,000,000,000 molecules

– 3.01 x 1023 molecules

• 0.00081 = 8.1 x 10-4

– Decimal moves 4 place to the right

• 34,000 = 3.4 x 104

– Decimal move 4 places to the left

Scientific Notation

To make these numbers easier to work with, we put them into scientific notation.

1) Rewrite the significant digits as a number greater than one, but less than 10.

2) Count the number of places you had to move the decimal to complete step 1.

3) Write the number of decimal places moved as an exponent.

A. Positive exponent greater than 1.B. Negative exponent less than 1.

Sample Problems

602 200 000 000 000 000 000 000

1) Rewrite as a number greater than one but less than 10.

6.0222) Count the number of places the decimal

moved. (left)23 places

3) Write that number as an exponent.6.022 x 1023

How about another one?0.000000000000000000000000000000911

1) Rewrite as a number greater than one but less than 10.

9.11

2) Count the number of places the decimal moved. (right) 31

3) Write that number as an exponent.

9.11 x 10-31

How about the other direction?

Speed of light in a vacuum is

3.00 x 108 m/s

Move the decimal 8 places to the right.

300 000 000 m/s

One last sample

Atomic Mass Unit

1.66054 x 10-27 kg

Move the decimal 27 places to the left.

0.00000000000000000000000000166054 kg

Significant Figures

a.k.a.- sig figs

Significant Digits

• The certain digits and one estimated digit of each measurement are significant.

Remember! Every time you make a measurement, you record all of the certain digits and one estimated digit.

200.54 g

Rules for Sig Figs

1) Non zeros are always significant.2) Zeros between non zeros are significant.3) Zeros at the end of significant digits following

a decimal point are significant.*They show precision in measurement.

4) Place keeper zeros are NOT significant.a) Zeros preceding significant digits.b) Zeros following significant digits without a

decimal point.

Try These Examples

7.05940Final zero significant (follows decimal point)

6 significant digits0.00135

Leading zeros Not significant (place keepers)3 significant digits

20,400Final zeros Not significant (place keepers – no decimal)

3 significant digits

Sig Figs and Calculations

Adding and Subtracting

Round to the fewest number of decimal

places given in problem. (Can only

have ONE estimated digit in final answer)

Multiplying and Dividing

Round to the fewest number of significant

digits given in the problem.

Sample Problems

17.20(.01) 4.137 (.001)

+ 26.6 (.1) 47.937 Least significant

number is reported to the tenths, so round final answer to the tenths.

47.9

14.3 (3 sig figs)

1.0200 (5 sig figs)

x 0.005 (1 sig fig)

0.07293

Fewest number of sig figs is one, so round the final answer to one sig fig.

0.07

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