1. Chapter 2 Measurements 2.2 Scientific Notation
Learning Goal Write a number in scientific notation.
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2. Scientific Notation
Scientific notation is used to write very large or very small numbers such as
the width of a human hair, m, which is also written as 8 × 10−6 m
the number of hairs on a human scalp, hairs, which is also written as 1 × 105 hairs
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3. Writing Numbers in Scientific Notation
A number written in scientific notation contains a coefficient and a power of ten.
coefficient power unit
of ten
× m
The coefficient is at least 1 but less than 10.
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4. Writing Numbers in Scientific Notation
The number of spaces moved to obtain a coefficient between 1 and 10 is shown as a power of ten.
= × 104
move decimal 4 spaces left
= × 10−3
move decimal 3 spaces right
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5. Some Powers of Ten
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6. Some Measurements in Scientific Notation
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7. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation Diameter of the Earth
m × 107 m
Mass of a human
68 kg × 101 kg
Diameter of a virus
cm 3 × 10−7 cm
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8. Scientific Notation and Calculators
You can enter a number written in scientific notation on many calculators using the EE or EXP key.
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9. Scientific Notation and Calculators
When a calculator display appears in scientific notation, it is shown as a number between 1 and 10, followed by a space and the power (exponent).
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10. Scientific Notation and Calculators
On many scientific calculators, a number is converted to scientific notation, using the appropriate keys.
nd or 3rd function key SCI
Key Key
= 5.2 −04 or 5.2−04 = 5.2 × 10−4
Calculator display
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11. Guide to Writing a Number in Scientific Notation
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12. Learning Check
Write the following number in the correct scientific notation, g.
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13. Move the decimal 5 places to the right, to give a coefficient of 5.8.
Solution
Write the following number in the correct scientific notation, g.
Step 1 Move the decimal point to obtain a coefficient that is at least 1 but less than
Move the decimal 5 places to the right, to give a coefficient of 5.8.
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14. Step 2 Express the number of places moved as a power of 10.
Solution
Write the following number in the correct scientific notation, g.
Step 2 Express the number of places moved as a power of 10.
Moving the decimal 5 places to the right gives a power of −5.
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15. Solution
Write the following number in the correct scientific notation, g.
Step 3 Write the product of the coefficient multiplied by the power of 10 with the unit. 5.8 × 10−5 g
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16. Select the correct scientific notation for each. A. 0.000 008
Learning Check
Select the correct scientific notation for each. A
(1) 8 × 106 (2) 8 × 10−6 (3) 0.8 × 10−5 B
(1) 7.2 × 104 (2) 72 × 103 (3) 7.2 × 10−4
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17. Select the correct scientific notation for each. A. 0.000 008
Solution
Select the correct scientific notation for each. A
(Move the decimal 6 places to right.)
(2) 8 × 10−6 B
(Move the decimal 4 places to the left.)
(1) 7.2 × 104
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18. Write each as a standard number. A. 2.0 × 10−2
Learning Check
Write each as a standard number.
A. 2.0 × 10−2
(1) 200 (2) (3) 0.020
B. 1.8 × 105
(1) (2) (3)
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19. Write each as a standard number. A. 2.0 × 10−2 (3) 0.020 B. 1.8 × 105
Solution
Write each as a standard number.
A. 2.0 × 10−2
(3) 0.020
B. 1.8 × 105
(1)
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