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.
To fulfill the demand for quickly locating and searching documents.
It is intelligent file search solution for home and business.
Related searches
- significant figures and scientific notation worksheets
- scientific notation significant figures worksheet
- scientific notation significant figures quiz
- scientific notation and significant figure worksheet answers
- scientific notation worksheet with answer key
- significant figures scientific notation rules
- significant figures and scientific notation worksheet
- significant figures scientific notation calculator
- convert scientific notation to real
- scientific notation chemistry
- scientific notation word
- scientific notation word problem pdf