Transcript Ch 4-5 Scientific Notation

4-5 Scientific Notation
Evaluating Algebraic Expressions
California
Standards
NS1.1 Read, write, and compare rational
numbers in scientific notation (positive and
negative powers of 10), compare rational
numbers in general.
4-5 Scientific Notation
The table shows relationships between several powers of
10.
Evaluating Algebraic Expressions
• Each time you divide by 10, the exponent in the
power decreases by 1 and the decimal point in the
value moves one place to the left.
• Each time you multiply by 10, the exponent in the
power increases by 1 and the decimal point in the
value moves one place to the right.
4-5 Scientific Notation
Evaluating Algebraic Expressions
You can find the product of a number and a
power of 10 by moving the decimal point of
the number. You may need to write zeros
to the right or left of the number in order
to move the decimal point.
4-5 Scientific Notation
Additional Example 1: Multiplying by Powers of
Ten
Evaluating Algebraic Expressions
Multiply.
A. 14  104
14.0 0 0 0
140,000
B. 3.6  10-5
0 0 0 0 3.6
0.000036
Since the exponent is a
positive 4, move the decimal
point 4 places to the right.
Since the exponent is a
negative 5, move the decimal
point 5 places to the left.
4-5 Scientific Notation
Check It Out! Example 1
Evaluating Algebraic Expressions
Multiply.
A. 2.5  105
2.5 0 0 0 0
250,000
B. 10.2  10-3
0 10.2
0.0102
Since the exponent is a
positive 5, move the decimal
point 5 places to the right.
Since the exponent is a
negative 3, move the decimal
point 3 places to the left.
4-5 Scientific Notation
Evaluating Algebraic Expressions
Powers of 10 are used when writing
numbers in scientific notation. Scientific
notation is a way to express numbers that
are very large or very small. Numbers
written in scientific notation are expressed
as 2 factors. One factor is a number
greater than or equal to 1. The other factor
is a power of 10.
4-5 Scientific Notation
Additional Example 2: Writing Numbers in
Scientific Notation
Evaluating
Algebraic
Expressions
Write
the number in
scientific notation.
A. 0.00709
Think: The decimal needs to move
3 places to get a number between 1
and 10.
7.09  10-3
Think: The number is less than 1, so
the exponent will be negative.
So 0.00709 written in scientific notation is 7.09  10–3.
4-5 Scientific Notation
Additional Example 2: Writing Numbers in
Scientific Notation
Evaluating
Algebraic
Expressions
Write
the number in
scientific notation.
B. 23,000,000,000
2.3  1010
Think: The decimal needs to
move 10 places to get a
number between 1 and 10.
Think: The number is greater
than 1, so the exponent will
be positive.
So 23,000,000,000 written in scientific notation is
2.3  1010.
4-5 Scientific Notation
Check It Out! Example 2
Write
the number Algebraic
in scientific notation.
Evaluating
Expressions
Think: The decimal needs to
move 4 places to get a
number between 1 and 10.
A. 0.000811
8.11  10
-4
Think: The number is less
than 1, so the exponent will
be negative.
So 0.000811 written in scientific notation is 8.11  10–4.
4-5 Scientific Notation
Check It Out! Example 2
Evaluating
Algebraic
Expressions
Write
the number in
scientific notation.
B. 480,000,000
4.8  108
Think: The decimal needs to
move 8 places to get a number
between 1 and 10.
Think: The number is greater
than 1, so the exponent will
be positive.
So 480,000,000 written in scientific notation is
4.8  108.
4-5 Scientific Notation
Additional Example 3: Reading Numbers in
Scientific Notation
Evaluating
Expressions
Write
the number Algebraic
in standard form.
A. 1.35  105
1.35  105
1.35000
135,000
Think: Move the decimal right 5
places.
4-5 Scientific Notation
Additional Example 3: Reading Numbers in
Scientific Notation
Evaluating Algebraic Expressions
Write the number in standard form.
B. 2.7  10–3
2.7  10–3
0002.7
0.0027
Think: Move the decimal left 3
places.
4-5 Scientific Notation
Check It Out! Example 3
Evaluating Algebraic Expressions
Write the number in standard form.
A. 2.87  109
2.87  10 9
2.870000000
2,870,000,000
Think: Move the decimal
right 9 places.
4-5 Scientific Notation
Check It Out! Example 3
Evaluating Algebraic Expressions
Write the number in standard form.
B. 1.9  10–5
–5
1.9  10
000001.9
0.000019
Think: Move the decimal left 5
places.
4-5 Scientific Notation
Additional Example 4: Comparing Numbers in
Scientific Notation
Evaluating
Expressions
A certain
cell has aAlgebraic
diameter of approximately
4.11  10-5 meters. A second cell has a diameter
of 1.5  10-5 meters. Which cell has a greater
diameter?
4.11  10-5
1.5  10-5
Compare the exponents.
4.11 > 1.5
Compare the values between
1 and 10.
Notice that 4.11  10-5 > 1.5  10-5.
The first cell has a greater diameter.
4-5 Scientific Notation
Check It Out! Example 4
A star has a diameter of approximately
Evaluating
Algebraic Expressions
3
5.11  10 kilometers. A second star has a
diameter of 5  104 kilometers. Which star has
a greater diameter?
5.11  103
5  104
Compare the exponents.
Notice that 3 < 4. So 5.11  103 < 5  104
The second star has a greater diameter.