Scientific

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Scientific Notation
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Objectives and Vocabulary

1. Be able to write a number in scientific notation
   when given the decimal form of the number.
2. Be able to write a number in decimal form when
   given the number in scientific notation.
3. Perform mathematical calculations involving
   scientific notation.
4. Solve problems using scientific notation.

Decimal form A number written with place values
corresponding to powers of ten such as 152, 9.5,
0.08. Scientific notation a number expressed in
the form c x 10n where n is an integer and 1? c ?
10.
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Writing in Decimal Form
Write the following number in decimal form.
This expression can be rewritten as
Furthermore
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Positive Powers of 10
Positive powers of 10 When the exponent (n) is
positive, move the decimal point to the right the
same number of places as the exponent. Add zeros
when digits are not present.
Write the following numbers in decimal form
Solutions
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Dividing by 10
Write the following number in decimal form.
This expression can be rewritten as
Furthermore,
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Negative Powers of 10
Negative powers of 10 When the exponent (n) is
negative, move the decimal point to the left the
same number of places as the absolute value
exponent. Add zeros when digits are not present.
Write the following numbers in decimal form
Solutions
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Writing in Scientific Notation

1. Move the decimal point to the right or left until
   you have a number that is greater than or equal
   to 1, but less than 10.
2. Count how many places you moved the decimal
   point. This number will become the absolute
   value of the exponent.
3. If you moved the decimal point to the left, the
   exponent will be positive.
4. If you moved the decimal point to the right, make
   the exponent negative.

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Examples
Write the following numbers in scientific
notation.
Solutions

1. The decimal is to the right of the 3. Move it
   left 3 places.

1. This number is already greater than or equal to
   one and less than 10. Therefore, the decimal
   doesnt have to be moved and the exponent will be
   0

1. Move the decimal right 4 places.

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Using a calculator
Use a calculator to perform the indicated
operation. Write your result in correct
scientific notation.

1. Enter 9.1 in your calculator.
2. Press the key marked EXP or EE on your
   calculator. If this is written above another
   key, then you will have to press SHIFT or 2nd
   before pressing the EXP or EE key.
3. Enter the value of the exponent.
4. Press the times key.
5. Enter 4.2
6. Repeat steps 2 and 3.
7. Press Enter or . You should get 3.822x10-1

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You Try It

1. Decide whether the number is in scientific
   notation. If not, tell why the number is not in
   correct scientific notation

1. Write the following numbers using scientific
   notation

1. Write the following numbers in decimal form

1. Atoms are composed of protons, neutrons and
   electrons. If the mass of protons and neutrons
   are each 1.67 x 10-24 grams and an electron has a
   mass of 9.11 x 10-28 gram. Find the mass of an
   atom of silver which has 47 protons, 47
   electrons, and 60 neutrons.

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Problem 1

1. This number is not written correctly in
   scientific notation. The value of c is supposed
   to be greater than or equal to 1and less than 10.
   Here, the value of c is less than 1.
2. This number is not correctly written using
   scientific notation because the power of 10 is
   supposed to be an integer. Thus, it cant be a
   fraction.
3. This number is correctly written using scientific
   notation

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Problem 2
The decimal had to be moved left three places so
the power of ten is positive 3.
The decimal had to be moved to the right two
places, so the power of ten is negative two.
The decimal does not need to be moved.
Therefore, the power of ten is zero.
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Problem 3
The decimal point had to be moved two places to
the left because the power of ten was negative
two.
The decimal point had to be moved six places to
the right because the power of ten was positive
six
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Problem 4

1. Find the mass of the protons.

1. Find the mass of the neutrons.

1. Find the mass of the electrons.

1. Add the values together from steps 1-3 to get the
   final answer.