Scientific Notation and Conversions
Chapter 1 section 7
Scientific Notation
Page 82
Use
•
Very large numbers
•
Space flight
•
Distance
•
Government
•
Budget
•
Population
•
Very small numbers
•
Microbiology
•
Virus
•
Oxygen molecules
•
Hydrogen atom
Scientific Notation
Example
6.4 x 10
3
means 6 400
2.17 x 10
-3
means 0.00217
Note: numbers with a positive exponent is
relatively large
and
number with the negative exponent is
relatively small
Scientific to Decimal Notation
a x 10
n
•
Use the exponent, n
If positive, move the decimal point in ‘a’ to the
right, n places
If negative, move the decimal point in ‘a’ to
the left |n| places.
Example
Change to a decimal
a)
6.2 x 10
7
since n = 7 is positive, move the decimal point
in 6.2, 7 places to the right so
62 000 000
b) 2.019 x 10
-3
since n = -3 is negative, move the decimal
point in 2.019, 3 places to the left.
0.002 019
Try. Change to decimal
1)
9.2 x 10
2
2) -8.17 x 10
6
3)
-4.15 x 10
-3
4)
6.8 x 10
-5
Decimal to Scientific Notation
1)
Write the number between 1 and 9
2)
Write the power of 10. Count the number of
places the decimal point moved.
3)
Large number, positive exponent, small number,
less than 1, negative exponent
Change to Scientific Notation
a)
34,970,000
Write the number between 1 – 9
3.497
Count the number of places the decimal point was
moved. This is the exponent: 7 places
Since it is a large number, the exponent is positive
so 3.497 x 10
7
Change to Scientific Notation
0.00000745
Write the number between 1 and 9
7.45
Count the number of decimal places that the
decimal point was moved. 6 places
Since the number is small, the exponent is
negative
7.45 x 10
-6
Change to Scientific Notation
5) 32 000
6) 0.007
7) - 0.000 000 57
Computation with Scientific
Notation
Compute with Scientific Notation
a)
(6.1 x 10
5
)(4 x 10
-9
)
Solution
(6.1 x 4) x (10
5
x 10
-9
)
24.4 x 10
5 +(-9)
24.4 x 10
-4
2.44 x 10
1
x 10
-4
2.44 x 10
-3
Compute with Scientific Notation
Compute with Scientific Notation
Formula for Motion
d = rt
Distance equals rate times time
Motion problem
Light travels at a rate of approximately 1.86 x 10
5
miles per second. It takes light 5 x 10
2
seconds to
travel from the sun to earth. What is the distance
between earth and the sun?
Summary
•
Decimal to scientific notation
•
Scientific notation to decimal
•
Computations using scientific notation
Scientific notation is a useful way to express very large or very small numbers in a concise form. This chapter discusses how to convert numbers between scientific notation and decimal notation, providing examples and explanations for better understanding.
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Presentation Transcript
Chapter 1 section 7 Scientific Notation Page 82
Use Very large numbers Space flight Distance Government Budget Population Very small numbers Microbiology Virus Oxygen molecules Hydrogen atom
Scientific Notation Expressed in the form a x 10? Where the absolute value of a is greater than or equal to 1 and less than 10, ( 1 |a| < 10) and n is an integer Customary to use multiplication symbol, x, rather than a dot.
Example 6.4 x 103means 6 400 2.17 x 10-3means 0.00217 Note: numbers with a positive exponent is relatively large and number with the negative exponent is relatively small
Scientific to Decimal Notation a x 10n Use the exponent, n If positive, move the decimal point in a to the right, n places If negative, move the decimal point in a to the left |n| places.
Example Change to a decimal a) 6.2 x 107 since n = 7 is positive, move the decimal point in 6.2, 7 places to the right so 62 000 000 b) 2.019 x 10 -3 since n = -3 is negative, move the decimal point in 2.019, 3 places to the left. 0.002 019
Try. Change to decimal 1) 9.2 x 102 2) -8.17 x 106 3) -4.15 x 10-3 4) 6.8 x 10-5
Decimal to Scientific Notation 1)Write the number between 1 and 9 2)Write the power of 10. Count the number of places the decimal point moved. 3)Large number, positive exponent, small number, less than 1, negative exponent
Change to Scientific Notation a) 34,970,000 Write the number between 1 9 3.497 Count the number of places the decimal point was moved. This is the exponent: 7 places Since it is a large number, the exponent is positive so 3.497 x 107
Change to Scientific Notation 0.00000745 Write the number between 1 and 9 7.45 Count the number of decimal places that the decimal point was moved. 6 places Since the number is small, the exponent is negative 7.45 x 10-6
Change to Scientific Notation 5) 32 000 6) 0.007 7) - 0.000 000 57
Computation with Scientific Notation
Compute with Scientific Notation a) (6.1 x 105)(4 x 10-9) Solution (6.1 x 4) x (105x 10-9) 24.4 x 10 5 +(-9) 24.4 x 10-4 2.44 x 10 1x 10-4 2.44 x 10-3
Compute with Scientific Notation 1.8 ? 104 3 ? 10 2 b) 1.8 3x 104 0.6 x 104 2 0.6 x 106 6.0 x 10 1x 106 6.0 x 105 10 2
Compute with Scientific Notation 8) ( 2 x 104)(4.3 x 103) 9) (5.1 x 10- 8)(3 x 10- 4) 10) 2.4 ? 10 2 4.8 ? 106
Formula for Motion d = rt Distance equals rate times time
Motion problem Light travels at a rate of approximately 1.86 x 105 miles per second. It takes light 5 x 102seconds to travel from the sun to earth. What is the distance between earth and the sun?
Summary Decimal to scientific notation Scientific notation to decimal Computations using scientific notation
