STANDARD FORM - Cooper Blog · Think: The decimal needs to move left to change 7.09 to 0.00709, so...
Transcript of STANDARD FORM - Cooper Blog · Think: The decimal needs to move left to change 7.09 to 0.00709, so...
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STANDARD FORM SCIENTIFIC NOTATION
9,200,000,000,000,000
.0000000000254
-23,000,000,000
-.000091
9.2 x 1015
2.54 x 10-11
-2.3 x 1010
-9.1 x 10-5
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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.
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1. Find a number bigger than 1, less than 10
a. Only 2 decimal places b. This is your NEW
decimal
2. Multiply by 10 ( x 10) 3. Count decimal spaces
from NEW to OLD (this is your exponent on 10)
4. LEFT = POSITIVE RIGHT = NEGATIVE (exponent)
82,000,000 1. 8.2
2. 8.2 x 10
3. 7 Spaces (8.2 x 107)
4. LEFT
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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.
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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
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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
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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:
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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)
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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
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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
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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**
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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