SCIENTIFIC NOTATION



SCIENTIFIC NOTATION

Notes & Practice

Astronomy deals with very large and very small numbers...like this:

(0.000000000000000000000000000000663 x 30,000,000,000) ÷ 0.00000009116

Y I K E S ! !

In scientific notation it looks like this: (6.63 x 10¯31 x 3.0 x 1010) ÷ 9.116 x 10¯8

Format for Scientific Notation

1. Scientific Notation is used to represent positive numbers only.

2. There are two parts to a number written in scientific notation:

a. A number between 1 and 9 with two places to the right of the decimal

b. An exponent

A.BC x 10some positive or negative integer

3. Other examples:

• 0.00087 becomes 8.7 x 10¯4

• 9.8 becomes 9.8 x 100 (the 100 is seldom written)

• 23,000,000 becomes 2.3 x 107

• 0.000000809 becomes 8.09 x 10¯7

• 4.56 becomes 4.56 x 100

• 250,000,000,000 becomes 2.50 x 1011

Exponent Definitions & Rules

If a whole number has no decimal, it is placed to the right of the last digit. 56 = 56.0

103 = 10 x 10 x 10 = 1000

102 = 10 x 10 = 100 positive exponents make the number larger

move the decimal to the right

101 = 10

100 = 1

10-1 = 1(10 = .01 negative exponents indicate fractions

make the number smaller

10-2 = 1((10 x 10) = 1(100 = 0.01 move the decimal to the left

10-3 = 1((10 x 10 x 10) = 1(1000 =0.001

To multiply exponents, add them: 103 x 102 = 10 3+2 = 105

To divide exponents, subtract them: 104 ( 102 = 10 4-2 = 102

If there are exponents in parenthesis, multiply them: (103)2 = 10(3x2) = 106

Practice #1 - Convert 29,190,000,000 to scientific notation.

29,190,000,000 = 2.919 x 10,000,000,000 = 2.919 x 1010 = 2.92 x 1010

Practice #2 - Write 0.00000000459 in scientific notation.

0.00000000459 = 4.59 x 0.000000001 = 4.59 x 10¯9

Practice #3 - Convert 428.5 x 109 to scientific notation.

Step 1 - convert the 428.5 to scientific notation. Answer = 4.285 x 102.

Step 2 - write out the new number. Answer = 4.285 x 102 x 109.

Step 3 - combine the exponents according to the usual rules for exponents.

Answer = 4.285 x 1011.

Practice #4 - Convert 208.8 x 10¯11 to scientific notation.

Step 1 - convert the 208.8 to scientific notation. Answer = 2.088 x 102.

Step 2 - write out the new number. Answer = 2.088 x 102 x 10¯11.

Step 3 - combine the exponents according to the usual rules for exponents.

Answer = 2.088 x 10¯9.

Practice Problems

Convert to scientific notation:

1) 28,000,000

2) 305,000

3) 0.000000463

4) 0.000201

5) 3,010,000

6) 0.000000000000057

7) 20,100

8) 0.00025

9) 65,000,000,000,000,000

10) 8.54 x 1012

11) 2101 x 10¯16

12) 305.1 x 107

13) 0.0000594 x 10¯16

14) 0.00000827 x 1019

15) 386 x 10¯22

16) 2519 x 1012

17) 0.000482 x 10¯12

18) 0.00003213 x 1012

19) 2887 x 105

20) 4.05 x 1011

The answers:

1) 2.8 x 107

2) 3.05 x 105

3) 4.63 x 10¯7

4) 2.01 x 10¯4

5) 3.01 x 106

6) 5.7 x 10¯14

7) 2.01 x 104

8) 2.5 x 10¯4

9) 6.5 x 1016

10) already in scientific notation

11) 2.10 x 10¯13

12) 3.05 x 109

13) 5.94 x 10¯21

14) 8.27 x 1013

15) 3.86 x 10¯20

16) 2.52 x 1015

17) 4.82 x 10¯16

18) 3.21 x 107

19) 2.89 x 107

20) already in scientific notation

SCIENTIFIC NOTATION

Notes & Practice

Astronomy deals with very large and very small numbers...like this:

(0.000000000000000000000000000000663 x 30,000,000,000) ÷ 0.00000009116

Y I K E S ! !

In scientific notation it looks like this:

Format for Scientific Notation

1. Scientific Notation is used to represent ____________________ numbers only.

2. There are two parts to a number written in scientific notation:

a. ________________________________________________________________

b. ________________________________________________________________

3. Other examples:

• 0.00087 =

• 9.8 =

• 23,000,000 =

• 0.000000809 =

• 4.56 =

• 250,000,000,000 =

Exponent Definitions & Rules

If a whole number has no decimal, it is placed to the __________ of the last digit.

103 =

102 =

101 =

100 =

10-1 =

10-2 =

10-3 =

To multiply exponents, _______________ them:

To divide exponents, _______________ them:

If there are exponents in parenthesis, _______________ them:

Practice #1 - Convert 29,190,000,000 to scientific notation.

Practice #2 - Write 0.00000000459 in scientific notation.

Practice #3 - Convert 428.5 x 109 to scientific notation.

Step 1 -

Step 2 -

Step 3 -

Practice #4 - Convert 208.8 x 10¯11 to scientific notation.

Step 1 –

Step 2 -

Step 3 -

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download