Scientific Notation

Advantages of scientific notation

1. Allows for very large and very small numbers to be written in a more manageable form

2. It can make calculations with very large and very small numbers easier if a calculator is not available

The general format of scientific notation is

N x 10y

Where 1< N < 10

And y indicates the number of places and direction the decimal moves

Positive exponents

To convert 1234000.000 into scientific notation we move the decimal behind the first number. Count the number of places moved and that number becomes the exponent on the 10.

1234000 000.

1.234000000 x 106

And you get

To put the number back into regular notation you move the decimal back to the right the number of places stated by the exponents

The exponent is 4, therefore the decimal moves 4 places.

And you get 36780

3 678.3 678 x 104

Negative Exponents

• To convert 0.00123 into scientific notation, we move the decimal behind the first non-zero digit.

0 00123.

The number of spaces moved becomes the exponent on the 10, but as a negative.

1.23 x 10-3

Scientific Notation

• Converting into Sci. Notation:

– Move decimal until there’s 1 digit to its left. Places moved = exponent.

– Large # (>1) positive exponentSmall # (<1) negative exponent

– Only include sig figs.

65,000 kg 6.5 × 104 kg

Scientific Notation

• Calculating with Sci. Notation

(5.44 × 107 g) ÷ (8.1 × 104 mol) =

5.44EXPEXP

EEEE÷÷

EXPEXP

EEEE ENTERENTER

EXEEXE7 8.1 4

= 671.6049383 = 670 g/mol = 6.7 × 102 g/mol

Type on your calculator:

Using a Calculator

• Type in the number• Press Exp and enter

the exponent value• DO NOT MULTIPLY

BY 10. The exp does that for you.

• Type in the number• Press Exp and enter

the exponent value• DO NOT MULTIPLY

BY 10. The exp does that for you.

• Type in the number• Press EE and enter

the exponent value• DO NOT MULTIPLY

BY 10. The EE does that for you.

• Type in the number• Press 2nd x-1 and

enter the exponent value

• DO NOT MULTIPLY BY 10. The 2nd x-1

does that for you.

• Type in the number• Press Exp and enter

the exponent value• DO NOT MULTIPLY

BY 10. The exp does that for you.

Copying Answers from a calculator

2E7

If answer on calculator looks like this

27

Do not write it like that!!!

X X

Instead, write it as 2 x 107

Practice Problems

1. (7.35X10-11)(3.21X1023)(1.69X10-19)(9.6X103)(7.15X1015)(25.7)

1. (0.000357)(757391)(250(7531)(2.53X1021)

1. (3.576X10-5)(6.35X107)(523)(32571)(7.55X1057)

= 2.3X10-27

=3.5X10-21