Transcript Lesson 2 - GEOCITIES.ws

Lesson 2
Scientific Notation
 Scientific notation is a special way of
writing numbers. It is used in many
different fields of science to show very large
and very small numbers.
 Here are three numbers and their
equivalents in scientific notation
230,000 = 2.3 x 105
0.00000105 = 1.05 x 10-6
4,761,000,000 = 4.761 x 109
 A number in scientific notation has two
factors:
 A number greater than or equal to 1 and less
than 10.
 A power of 10 (10 with an exponent). The
exponent can be either positive or negative.
Large numbers get positive exponents; very
small numbers get negative exponents.
Example 1
 Saturn is about 875,000,000 miles from the
sun. How would this distance be
represented in scientific notation?
 Strategy: Write the number, using the two
factors for scientific notation.
 Step 1: Write the first factor by using the
three non-zero digits (875) 0f 875,000,000.
Place a decimal point after the first digit.
The first factor becomes 8.75. Remember,
this factor is a number greater than or equal
to 1 but less than 10.
 Step 2: What number times 8.75 equals
875,000,000? The number is 100,000,000
or 108, so 108 is the second factor. A quick
way to find the exponent of 10: Count the
number of places after the first digit in
875,000,000. There are 8 places. So, the
exponent of 10 is 8.
 Step 3: Write the two factors together:
875,000,000 = 8.75 x 108
Solution
 The distance of Saturn from the sun is
8.75 x 108 miles.
Note: The exponent 8 in the answer
represents 8 places to the left from the
original decimal point (875,000,000).
8.75,000,000.
count 8 places to the left
Finding the Exponent for the
Second Factor
 Count the number of places from the
original decimal point to the decimal point
of the first factor.
 Rule 1: If you count to the left from the
original decimal point, the exponent is
positive.
 Rule 2: If you count to the right from the
original decimal point, the exponent is
negative.
Example 2
 Write 0.00017 in scientific notation.
 Step 1: Use the two non-zero digits of
0.00017 to write the first factor. The two
non-zero digits are 1 and 7. The first factor
is a number  1 but < 10. In this case 1.7 is
the first factor.
 Step 2: Use the rule to find the power of 10
for the second factor.
.0001.7
count 4 places to the right
The power of 10 is -4. (Rule 2 states that if
you count to the right, the exponent is
negative.)
 Step 3: Write the two factors together.
Solution
 The number 0.00017 expressed in scientific
notation is 1.7 x 10-4.
 You often see (in newspapers and books) a
large number abbreviated using a mix of
numbers and words. Instead of the number
4,500,000, you see 4.5 million. This form is
similar to scientific notation, since it starts
with a number between 0 and 10.
Example 3
 For the number 9,600,000 write the number
in mixed number-word form.
 Strategy: Use scientific notation.
 Step 1: What is the beginning number in
scientific notation for 9,600,000? The
number 9,600,000 in scientific notation is
9.6 x 106. The beginning number is 9.6
 Step 2: What is the value of 106?
106 = 1,000,000 or 1 million.
Solution
 9,600,000 = 9.6 million
 You can convert the answers to traditional
multiplication problems into scientific
notation.
Example 4
 Express the product of 400 x 5000 in
scientific notation.
 Strategy: Find the product, and then change
it into scientific notation.
 Step 1: Multiply 400 x 5000
2,000,000
 Step 2: What is 2,000,000 in scientific
notation?
2 x 106
Solution
 2,000,000 = 2 x 106