Scientific Notation
1. Each row in the table has equivalent forms of the same number. Complete the following
table so that it makes sense.
Whole Number/Fraction
Decimal
Power of Ten
1000
1000
10 3
100
100
10 2
10
10
101
1
1
1
10
1
100
1
1000
0.1
2. In our place value system, each position represents some power of ten. Consider 123.456.
Which digit is in the 10 0 position? What is the value of the digit?
Which digit is in the 10 2 position? What is the value of that digit?
Which digit is in the 10 2 position? What is the value of that digit?
3. When the newspaper reports that the government spent 23.8 million dollars on education,
what does that number mean? Is it exact?
4. Fill in the blanks so that each number means 2,467,893,105.
________________ billion
______________ million
___________ thousand
5. The national debt is currently $7,613,772,338,689.34 (1/19/05), Write this amount out in
words. Why do you think the newspapers report this as $7.6 trillion?
6. Very large and very small numbers are difficult to read. So the newspaper shorthand makes
it easier to read those numbers. Mathematicians, scientists, engineers, and others who have
to deal with very large and very small numbers use a related type of shorthand known as
scientific notation.
$5,682,269,504,867.72 could be written in scientific notation as 5.7 x 1012 . Explain why you
think this notation means the same as 5.7 trillion.
7. A number written in scientific notation is a product of two numbers: (1) a number greater
than 1 and less than 10, and (2) a power of 10.
Consider 40,000. That number can be written as 4 x 10,000. In scientific notation, that
would be 4 x 10 4
2,360,000,000 can be written as 2.36 x 1,000,000,000 or 2.36 x 10 9 .
Write 0.0003 in words.
0.0003 can be written as 3 x 0.0001 or 3x 10 4 .
What do you notice about the relationship between the place value position of the leftmost
non-zero digit and the power of ten?
8. Convert each of these numbers written in standard form to scientific notation:
600
56,780,000,000
0.04
0.00000000000023
9. Convert each of these numbers written in scientific notation into standard form:
6.23 10 6
4.8  108
10. Scientific notation gives us a convenient way to multiply and divide very large numbers and
very small numbers. Complete the chart shown here and then write a description of how to
multiply numbers written in scientific notation.
Factor 1
4 102
5 10 2
1.5 10 4
Factor 2
2 103
3 10 4
6 102
Product (Sci. Not.)
Product (Standard)
11. Complete the chart shown here and then write a description of how to divide numbers
written in scientific notation.
Dividend
8 103
3 103
6 102
Divisor
2 104
6 102
4 10 3
Quotient (Sci. Not.)
Quotient (Standard)