Scientific Notation

& Standard Form

Let’s compare the two…

STANDARD FORM

• 9,200,000,000,000,000

• .0000000000254

• -23,000,000,000

• -.000091

SCIENTIFIC NOTATION

• 9.2 x 1015

• 2.54 x 10-11

• -2.3 x 1010

• -9.1 x 10-5

1. An ordinary quarter contains about 97,700,000,000,000,000,000,000 atoms.

2. The average size of an atom is about 0.00000003 centimeters across.

These very long numbers are written in **STANDARD FORM**

**The length of these numbers in standard notation makes them awkward to work with.

Scientific notation is a shorthand way of writing numbers – instead of standard notation.

Standard Form Scientific Notation

1. Find a number greater than or equal to 1, but less than 10

2. Multiply by 10 ( x 10) 3. Count decimal spaces

from NEW to OLD (this is your exponent on 10)

4. LEFT = NEGATIVE RIGHT = POSITIVE (exponent)

82,000,000 1. 8.2

2. 8.2 x 10

3. 7 Spaces (8.2 x 107)

4. Right

In scientific notation the number of atoms in a quarter (97,700,000,000,000,000,000,000 ) is

9.77 1022

and the size of each atom (0.00000003) is

3.0 10–8 centimeters across.

Think: The decimal needs to move left to change 7.09 to 0.00709, so the exponent will be negative.

0.00709

Move the decimal to get a number between 1 and 10.

7.09 10 Set up in scientific notation.

Check 7.09 10–3 = 7.09 0.001 = 0.00709

Write 0.00709 in scientific notation.

So 0.00709 written in scientific notation is 7.09 10–3.

Example 2:

(*you want only one number behind the decimal)

Think: The decimal needs to move 3 places

A pencil is 18.7 cm long. If you were to lay 10,000 pencils end-to-end, how many millimeters long would they be? Write the answer in scientific notation.

187 mm 10,000

1 cm = 10 mm 18.7 cm = 187 mm Multiply each side by 10

1,870,000 mm

Find the total length.

Multiply

Example 3:

Hint: 1. Convert from cm to mm 2. Find the length of 10,000

pencils

K H D M D C M

Think: The decimal needs to move 6 places.

In scientific notation the 10,000 pencils would be 1.87 106 mm long, laid end-to-end.

1.87 106 Set up scientific notation.

Think: The decimal needs to move right to change 1.87 to 1,870,000, so the exponent will be positive.

Example 3 continued:

Scientific Notation Standard Form

The exponent on the 10 tells you how many spaces you will move the decimal

If the exponent is POSITIVE move RIGHT

If the exponent is NEGATIVE move LEFT

EXAMPLES:

3.75 x 109 = 3,750,000,000

8.62 x 10-6 = .00000862

(5.23 X 107)

135,000

1.35

Think: Move the decimal right places.

A. 1.35 105

1.35 105

105 =

Write the number in standard notation:

A positive exponent means move the decimal to the right, and a negative exponent means move the decimal to the left.

Helpful Hint

100,000 100,000

5

Example 1:

BECAUSE

0.0027

by the reciprocal. 2.7 1000

Think: Move the decimal left 3 places.

B. 2.7 10–3

10 -3 =

2.7 1

10x10x10

2.7 10–3

1 1000

Divide

Write the number in standard notation: Example 1: HINT: Just remember that since the exponent is negative we move the decimal to the left 3 spaces

C. -2.01 104

-20,100

Think: Move the decimal right 4 places.

-2.01 104

104 = 10,000 -2.01 10,000

Example 1: Write the number in standard notation:

HINT: It doesn’t matter that the number (-2.01) is negative – only the exponent changes things

**Because 4 is POSITIVE**

Quiz:

Write each number in standard notation.

1. 1.72 104

2. 6.9 10–3

4. 57,000,000

17,200

0.0069

3. 0.0053 5.3 10–3

5.7 107

Write each number in scientific notation.

5. Order the numbers from least to greatest: 2 10–4 , 9 10–5 , 7 10–5

7 10–5, 9 10–5, 2 10–4