Download Problem Set 1, due Sep 4

Problem Set 1, due Sep 4
Scientific notation is a convenient way to express very small or very large numbers. You may or may not
already be familiar with this notation, but we will be using it extensively in this class, so the following
questions are designed to help you brush up.
The numbers are written like:
2. × 109 or 5. × 10−2 or 1.3 × 104
The exponent (9, or -2 or 4, in these examples) tells you the number of times the other number must be
multiplied by 10. So 1 × 103 is 1 × 10 × 10 × 10 = 1000. In practice, this means that the exponent tells you
the number of zeros or spaces to put before or after the decimal point.
Working with positive exponents
For positive exponents, move the decimal point to the right the number of spaces indicated by the exponent,
and place zeros in any space that doesn’t have a number in it. For example:
2. × 109 = 2 0 0 0 0 0 0 0 0 0. = 2000000000.
1.3 × 104 = 1 3 0 0 0. = 13000
Be careful. The exponent is not necessarily equal to the number of zeros! Got the hang of it? Try these:
a) 2 × 103 =
b) 4 × 105 =
c) 1.6 × 102 =
d) 8.76 × 101 =
Working with negative exponents
For negative exponents, move the decimal to the left the number of spaces indicated by the exponent, and
place zeros in any space that doesn’t have a number in it. For example:
5. × 10−2 = 0.0 5 = 0.05
7.83 × 10−5 = 0.0 0 0 0 7 8 3 = 0.0000783
Again, be careful. The exponent tells you how many spaces to move the decimal point- NOT how many
zeros there are in the number. Give these a try:
a) 5. × 10−5 =
b) 3. × 10−2 =
c) 1.965 × 100 =
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Some conventions
If the number only has an exponential part, for example 105 or 10−2 , these are equivalent to 1. × 105 or
1. × 10−2 .
By convention, scientific notation is written with exactly one number to the left of the decimal point.
For example, one would write 1.54 × 10−2 instead of 15.4 × 10−3 . But it’s easy to convert between the two.
Just move the decimal point to the left and add 1 to the exponent, or move the decimal point to the right
and subtract 1 from the exponent. Try writing the following numbers in the conventional scientific notation
(one number to the left of the decimal place).
a) 156.34 × 105 =
b) 0.0019 × 103 =
c) 398. × 10−6 =
Common words and prefixes
Exponents in scientific notation are associated with specific words and prefixes. For example, ‘centi’ refers
to 10−2 , so a ‘centimeter’ is 1. × 10−2 or 0.01 meters. Replace the following words in parentheses with the
correct number in scientific notation (look up the definitions of any words or prefixes you don’t know).
The Earth is (four and a half billion)
years old.
The solar system took about (10 million)
years to form.
An atom has a diameter of approximately (1 Angstrom)
meters.
meters wide.
A human hair is about (50 micro-)
meters above sea level.
Mt. Everest is about (9 kilo-)
‘Nanotechnology’ refers to the creation of things that are (nano-)
meters in size.
Multiplication and division
Multiplying and dividing in scientific notation is actually pretty simple. Work with the numbers and exponents separately. First multiply or divide the numbers. Then add or subtract the exponents. For example,
2. × 105
= 2 × 102
1. × 103
because 2./1. = 2 and 5 − 3 = 2. Or,
6. × 10−3 × 2. × 105 = 12. × 102 (= 1.2 × 103 )
because 2 × 6 = 12 and −3 + 5 = 2. Try these:
a)
24.×1011
8.×106
=
b)
5.×105
1.×10−3
=
c) (3. × 107 ) × (2. × 102 ) =
2
A sense of scale
Fill in the blanks with the closest of the given possible answers. Please show your work in the margins, or
on an attached sheet.
Possible answers: the diameter of a volleyball (66 cm), the distance between home plate and the pitcher’s
mound in baseball (18.4 m), the length of a compact car (2.5 m), the length of a football field (100 m), the
distance from Pasadena to Fresno (3.5 × 105 m), the distance from Pasadena to Monrovia (2 × 104 m)
diameter of Earth (1.3 × 104 km) : diameter of sun (1.4 × 106 km) =
diameter of a quarter (2.3 cm) :
distance between sun and Earth (1 Astronomical Unit) : diameter of sun (0.0046 Astronomical Units)=
distance from PCC to the Rose Bowl (4 × 103 m) :
sun-Pluto distance (39 Astronomical Units):sun-Earth distance (1 Astronomical Unit) =
distance from Pasadena to San Francisco (6 × 105 m) :
sun-closest star distance (4 × 1016 meters) : sun-Pluto distance (39 Astronomical Units) =
distance from PCC to the Rose Bowl (4000 m) :
Energy
Fill in the blanks with one of the following possible answers: chemical bond, gravitational potential, kinetic,
thermal, nuclear.
energy.
Food contains
We can convert the energy in food to
energy to keep our body temperature at 98◦ .
energy when we exercise.
We can also convert the energy in food to
Exercising on flat ground is easier than climbing a hill because by climbing we must convert some food
energy to
energy.
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The Electromagnetic Spectrum
Use the diagram above (or see page 34 of your book) to answer the following questions.
Stars in a constellation known as the Pleiades are blue. Are these stars hotter or colder than our sun?
Explain.
Aldebaran is a bright reddish star in the night sky. Is this star hotter or colder than our sun? Explain.
Molecular clouds are clouds of dust and gas sitting between stars. These clouds emit light at radio wavelengths rather than visible wavelengths. Qualitatively, how hot or cold would you expect molecular clouds
to be? How would their temperature compare to things we discussed in class? (the sun, lava, body heat).
Explain.
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