Download 3.5 Convert Small Numbers to Scientific Notation

3.5 Convert Small Numbers to
Scientific Notation
Common Core Standards
8. EE.3 Use numbers expressed in the form of a single digit times an
integer power of 10 to estimate very large or very small quantities, and to
express how many times as much one is than the other. For example,
estimate the population of the United States as 3 × 108 and the population
of the world as 7 × 109, and determine that the world population is more
than 20 times larger.
WARM-UP
Evaluate the expressions.
1) 10 −1
2) 10 −2
1
3) 7 ×
10
4)
7 × 10
6)
3 × 10 −2
5)
1
3×
100
−1
Convert Small Numbers to Scientific
Notation
Is there an easier way to write the
following fraction and decimal?
19
1,000,000,000
.000000019
NOTES
When we multiply by reciprocals of the powers of 10
(divide by powers of 10) the decimal point moves the
other way – to the left.
Examples
Evaluate the expressions. Express your answer as a
fraction and decimal.
1
7×
10
1
7×
100
1
7×
1,000
NOTES
To write small numbers in scientific notation:
–  Move the decimal point to behind the first nonzero digit.
–  The number of moves equals the negative
exponent of 10.
Examples
Write the numbers in scientific notation.
.00058
.00004
.00607
EXAMPLES
The distance across a cell is .0000005 meters. Write
the distance in scientific notation.
NOTES
To change scientific notation back into decimal form,
the exponent tells you how many times and the
direction to move the decimal point.
Concept Check
Write the numbers in decimal form.
2.6 × 10 −3
7 × 10
−4
EXAMPLES
Write the numbers as both a decimal and a fraction.
4.7 × 10 −2
9 × 10 −3
NOTES
When numbers are in scientific notation, the largest
number always has the largest exponent.
-2 > -5.
Examples
Copy the larger number.
1.7 × 10
−4
1.7 × 10
−6
3.4 × 10−2
9.5 × 10−6
NOTES
Calculators usually write scientific notation using the
letter "E" for exponent.
Examples
Rewrite the number using a power of 10.
3.8 E -4
5.02 E -6
PRACTICE
Write in scientific notation.
.034
.00098
Write in decimal form.
7.2 × 10
5 × 10 −4
−3
Copy the largest of the numbers.
4.5 × 10−3
1.9 × 10−1
8.6 × 10−5
FINAL QUESTION
Copy the largest of the numbers.
5.7 × 10
−4
3.6 × 10−2
7.7 × 10−6