Scientist need to express either very small numbers or very large number * the mass of a proton in a Hydrogen atom 0.000 000 000 000 000 000 000 000.

SCIENTIFIC NOTATION

SCIENTIFIC NOTATION Scientist need to express either very

small numbers or very large number

* the mass of a proton in a Hydrogen atom • 0.000 000 000 000 000 000 000 000 001

673kg• A single gram of Hydrogen has 602 000 000 000 000 000 000 000 H atoms

SCIENTIFIC NOTATION To easily express the numeric value of large

and small numbers we use scientific notation.

Def: an expression of numbers in the formm x 10n, where m is equal to or greater than 1 and less than 10, and n is an integer.

SCIENTIFIC NOTATION Scientific notation has 2 parts.

m x 10 n

a. A coefficient – a number in which one digit is placed to the left of the decimal.

b. An exponent – a power of 10 by which the number is multiplied.

POSITIVE EXPONENT A positive exponent indicates the

number of times the coefficient must be multiplied by 10.

Each time the decimal place is moved one place to the left, the exponent is increased by one.

EXPRESS 1234.56 IN SCIENTIFIC NOTATION 1234.56 x 100

123.456 x 101

12.3456 x 102

1.23456 x103

NEGATIVE EXPONENTS A negative exponent indicates the

number of times a coefficient must be divided by 10.

Each time the decimal place is moved one place to the right, the exponent is decreased by one.

EXPRESS 0.006 57 IN SCIENTIFIC NOTATION 0.006 57 x 100

0.0657 x 10-1

0.657 x 10-2

6.57 x 10-3

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 230

2.3x102

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 5601

5.601 x103

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 14 100 000

1.41 x 107

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 56 million

5.6 x 107

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 0.450 13

4.5013 x 10-1

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 0.089

8.9 x 10-2

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 0.000 26

2.6 x 10-4

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 0.000 000 698

6.98 x 10-7

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION 12 thousandth

1.2 x 10-2

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION The speed of light in a vacuum is 299 792 458 m/s

* 2.997 924 58 x 108 m/s

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION The mean radius of Earth is

6 378km

* 6.378 x 103km

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION The density of Oxygen is

0.001 42 g/ml

* 1.42 x 10-3g/ml

EXPRESS THE FOLLOWING IN SCIENTIFIC NOTATION The radius of an Argon atom is

0.000 000 000 098m

9.8 x 10-11m