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A METHOD OF DEALING WITH

VERY LARGE AND VERY SMALL

NUMBERS IN SCIENCE

Very large numbers!

BOOM!

How far?

92 000 000 miles

Very small numbers!

How wide is an atom?

0.000 000 000 1 metres wide!

Made up of three parts: the coefficient, the base and the exponent.

A. Writing Numbers in Scientific Notation

5.67 x 105 coefficient    base exponent

1. The coefficient must be between 1 and 9.9999999999999999999999999999999

2. The base must be 10

3. The exponent shows how many places the decimal moved. 

5.67 x 105 coefficient    base exponent

B. Scientific Notation Rules:

Examples of Scientific Notation

363,000,000,000 = 3.63 x 1011

0.00035 = 3.5 x 10-4

Numbers larger than 1, the exponent is positive Example: 8.38 x 105 = 838,000

Numbers less than 1, the exponent is negative Example: 5.03 x 10-3 = 0.00503

C. Scientific Notation Exponents

92 000 000 79.2 10 ..

Add the decimal point

Between 1 and 10

The point moved 7 places

Move the point to get a number between 1 and 10

79.2 10 miles

D. Scientific Notation for Large Numbers

0.000 000 000 1

101 10 .

The point moved 10 places. Negative sign for small numbers.

Move the point to get a number between 1 and 10

-101 10 metres wide

E. Scientific Notation for Small Numbers

Examples of Scientific Notation

363,000,000,000 = 3.63 x 1011

0.00035 = 3.5 x 10-4

a. 700 m c. 0.0054 kg

b. 38 000 m d. 0.000 006 87 kg

Practice – Convert to Scientific Notation

7 x 102 m

3.8 x 104 m

5.4 x 10-3 kg

6.87 x 10-6 kg

=86 000 000 78.6 10

Zeros after the point aren’t needed.

The point moves 7 places to the right

8.60000000.

Hint:Add 7 zeros, although you probably won’t need them

all.

F. Changing back large numbers

G.Changing back small numbers

= 0.000 00516

-65.16 10 5.16000000.

Hint:Add 6 zeros to the left of

the number.

-6 so remember to move point left for small numbers.

a. 1.26 x 104 kg c. 9.02 x 103 kg

b. 5.36 x 10-2 m d. 7.6 x 10-5 m

Practice – Convert back to a number

12600 kg

0.0536 m

9020 kg

0.000076 m

H. Multiplying using Scientific Notation

To multiply numbers in scientific notation, multiply the coefficients then add the exponents

Move the decimal point so that the number is in scientific notation

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Examples: Multiplying in Scientific Notation

I. Dividing using Scientific Notation

To divide numbers written in scientific notation: – divide the coefficients then – subtract the exponent in the denominator

(bottom) from the exponent in the numerator (top) => “top – bottom” or “first – second”

Express the final answer in scientific notation

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Example: Dividing Numbers in Scientific Notation

If you have to move the decimal to the LEFT, Add to the exponent

12.6 x 103 = 1.26 x 104

If you have to move the decimal to the RIGHT, Subtract from the exponent

0.902 x 104 = 9.02 x 103

Hint for converting an answer to scientific notation

LARS: Left Add, Right Subtract

 

Practice – Multiplying and Dividing

1.2 x 1011

3 x 101 2 x 10-1

1.2 x 10-1