培美曲塞说明书Scientific Notation
People who work in scientific fields often have to u very large and very small numbers. Look at some examples in the following table:
Measurement Value
Density of air at 27°C and 1 atm pressure0.001 61 g/cm3
Radius of a calcium atom0.000 000 000 197 m
One light-year9 460 000 000 000 km
The mass of a neutron0.000 000 000 000 000 000 000 001 675 g You can e that measurements such as the would be awkward to write out repeatedly. Also, calculating with very long numbers is likely to lead to errors becau it’s so easy to miscount zeros and decimal places. To make the num-bers easier to handle, scientists express them in a form known as scientific nota-tion, which us powe
rs of 10 to reduce the number of zeros to a minimum.
Look at a simple example of the way that scientific notation works. Following are some powers of 10 and their decimal equivalents.
10Ϫ2ϭ0.01
10Ϫ1ϭ0.1
100ϭ1
101ϭ10
102ϭ100
Suppo we rewrite the values in the table using scientific notation. The num-bers become much less cumbersome.手机电源键坏了怎么开机
Measurement Value
Density of air at 27°C and 1 atm pressure 1.61 ϫ10Ϫ3g/cm3
Radius of a calcium atom 1.97 ϫ10Ϫ10m
One light-year9.46 ϫ1012km
Mass of a neutron 1.675 ϫ10Ϫ24g
签名设计学习CONVERTING QUANTITIES TO SCIENTIFIC NOTATION
Sample Problem1
Express the following measurements in scientific notation.
a.310 000 L
b.0.000 49 kg
Solution
ANAL YZE
What is given in the problem?two measured quantities
What are you asked to find?the measured quantities expresd in scientific
notation
Items Data
a b
Measured quantity310 000 L0.000 49 kg
Quantity expresd in scientific notation? L? kg
PLAN
What steps are needed to rewrite the quantities in scientific notation?
Move the decimal point in each value until there is only one nonzero digit to the left of it. This number becomes the coefficient, M.
Count the number of places the decimal was moved. If it moved to the left, the count is a positive number. If it moved to the right, the count is a negative number. Make this number, n, the exponent of 10.
Quantity written in long formϭMϫ10n
COMPUTE
a.Express 310 000 L in scientific notation
b.Express 0.000 49 kg in scientific notation.
EVALUATE a
b
Are units correct?
Is the quantity correctly expresd?
Practice
1.Express the following quantities in scientific notation:a.8 800 000 000 m ans: 8.8 ؋109m b.0.0015 kg ans: 1.5 ؋10؊3 kg
三亚著名景点c.0.000 000 000 06 kg/m 3ans: 6 ؋10؊11kg/m 3
d.8 002 000 Hz ans: 8.002 ؋106Hz
e.0.009 003 amp ans: 9.003 ؋10؊3amp
f.70 000 000 000 000 000 km ans: 7 ؋1016km
g.6028 L ans: 6.028 ؋103L h.0.2105 g ans: 2.105 ؋10؊1g
i.600 005 000 kJ/h ans: 6.000 05 ؋108kJ/h j.33.8 m 2ans: 3.38 ؋101m 2
Yes; the decimal was moved to the right four places to give a coeffi-cient of 4.9 and an expo-nent of ؊4.
Yes; the decimal was
moved to the left five places to give a coeffi-cient of 3.1 and an expo-nent of ؉5.
Yes; the original measure-ment was in kilograms.Yes; the original measure-ment was in liters.
CALCULATING WITH QUANTITIES IN SCIENTIFIC NOTATION
Sample Problem2
What is the total of the measurements 3.61؋104mm, 5.88؋103mm, and 8.1؋102mm?
Solution
ANAL YZE
What is given in the problem?three measured quantities expresd in scien-
tific notation
What are you asked to find?the sum of tho quantities
Items Data
Measured quantity 3.61 ϫ104mm 5.88 ϫ103mm8.1 ϫ102mm PLAN
What steps are needed to add the quantities?
Convert each quantity so that each exponent is the same as that on the quantity with the largest exp
onent. The quantities can then be added together. Make sure the result has the correct number of significant figures.
COMPUTE
3.61 ϫ104mm ϩ5.88 ϫ103mm ϩ8.1 ϫ102mm ϭ? mm
Convert the cond and third quantities to multiples of 104.
To convert 5.88 ϫ103mm:
5.88 ϫ103mm ϭMϫ104mm
Becau one was added to the exponent, the decimal point must be moved one place to the left.
Mϭ0.588
To convert 8.1 ϫ102mm:
蒜泥拌白肉菱形脸发型8.1 ϫ102mm ϭMϫ104mm
Becau two was added to the exponent, the decimal point must be moved two places to the left.
Mϭ0.081
中庸名句
Now the three quantities can be added, as follows:
3.61ϫ104mm
ϩ0.588 ϫ104mm
ϩ0.081 ϫ104mm
4.275 ϫ104mm
To express the result in the correct number of significant figures, note that the result should only contain two decimal places.
EVALUATE
Are the units correct?
Yes; units of all quantities were millimeters.
Is the quantity correctly expresd in scientific notation?
Yes; there is only one number to the left of the decimal point.
Is the quantity expresd in the correct number of significant figures?
Yes; the result was rounded to give two decimal places to match the least accu-rate measurement.
describe
Practice
1.Carry out the following calculations. Express the results in scientific notation
and with the correct number of significant figures.
a.4.74 ϫ104km ϩ7.71 ϫ103km ϩ1.05 ϫ103km ans: 5.62؋104km
b.2.75 ϫ10Ϫ4m ϩ8.03 ϫ10Ϫ5m ϩ2.122 ϫ10Ϫ3m ans: 2.477؋10؊3m
