Knippium Chemistry

Scientific Notation

1. In science, we deal with some very LARGE numbers:

1 mole = 602000000000000000000000

2. In science, we deal with some very SMALL numbers:

Mass of an electron =

0.000000000000000000000000000000091 kg

Imagine the difficulty of calculating the mass of 1 mole of electrons!

0.000000000000000000000000000000091 kg

x 602000000000000000000000

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Scientific Notation

A method of representing very large or very small numbers

Example: 2 500 000 000.

9 8 7 6 5 4 3 2 1

Step #1: Insert an understood decimal point

Step #2: Decide where the decimal must end up so that one

number is to its left

Step #3: Count how many places you bounce the decimal point

Step #4: Re-write

answer

2.5 x 10⁹

The exponent is the number of places

we moved the decimal

Another Example of

Scientific Notation

.0000579

5 4 3 2 1

Step #2: Decide where the decimal must end

up so that one number is to its left

Step #3: Count how many places you bounce

the decimal point

Step #4: Re-write

Answer: 5.79 x 10^-5

The exponent is negative because the number we started with was less than 1.

PERFORMING CALCULATIONS IN

SCIENTIFIC NOTATION

ADDITION AND SUBTRACTION

Not only does scientific notation give us a way of

writing very large and very small numbers, it allows

us to easily do calculations as well. Calculators

are very helpful tools, but unless you can do these

calculations without them, you can never check to

see if your answers make sense. Any calculation

should be checked using your logic, so don’t just

assume an answer is correct.

Rule for Multiplication

When you multiply numbers with scientific notation, multiply

The Coefficients together and add the exponents. The

base will remain 10.

Ex 1. Multiply (3.45 x 10⁷) x (6.25 x 10⁵)

1^st rewrite the problem as: (3.45 x 6.25) x (10⁷ x 10⁵)

2^nd multiply the coefficients and add the exponents:

21.5625 x 10¹²

3^rd change to correct scientific notation and round to correct significant digits: 2.16 x 10¹³

NOTE – we add one to the exponent because we moved the decimal one place to the left.

Remember that correct scientific notation has a coefficient that is less

than 10, but greater than or equal to one.

Ex. 2.

Multiply (2.33 x 10^-6) x (8.19 x 10³)

1st rewrite the problem as:

(2.33 x 8.19) x (10^-6 x 10³)

2nd multiply the coefficients and add the exponents:

19.0827 x 10^-3

3rd change to correct scientific notation and round to correct significant digits 1.91 x 10^-2

Rule for Division

When dividing with scientific notation, divide the

coefficients and subtract the exponents. The base will

remain 10.

Ex. 1 Divide 3.5 x 10⁸ by 6.6 x 10⁴

1^st rewrite the problem as: 3.5 x 10⁸
———
6.6 x 10⁴

2^nd Divide the coefficients and subtract the exponents to get:

0.530303 x 10⁴

3^rd Change to correct scientific notation and round to correct significant digits to get: 5.3 x 10³

Note – We subtract one from the exponent because we moved the decimal one place to the right.