Download Scientific Notation with Positive Powers of Ten

Scientific Notation with Positive
Powers of 10
Warm Up
Write each number in scientific notation.
1. 58,927
2. 1,304,000,000
3. 6,730,000
4. 13,300
Write each number in standard notation.
5. 4 x 105
6. 1.8499 x 109
7. 6.41 x 103
8. 8.456 x 107
You can use scientific notation to
express very large quantities by writing
the large quantity as the product of a
number greater than or equal to 1 and
less than 10 and a power of 10.
• When you write 9 × 107 in standard notation,
how many zeros do you write?
• If you were to write 9 × 102 in standard
notation, how many zeros would you write?
• The standard notation for 9.3 × 107 is
93,000,000. Why are there 6 zeros instead of 7
zeros in the standard notation?
The average distance from Earth to
Mars is about 140,000,000 miles.
Write this distance in scientific
notation.
• Scientific notation is used to represent very large
numbers.
• One very large named number is a googol – the
number 1 followed by 100 zeros.
• An even larger named number is the googolplex – the
number 1 followed by a googol (10100) of zeros.
• This massive number can be represented as 10googol.
• This idea has been extended even further to name a
googolplexian, which is the number 1 followed by a
googolplex of zeros.
• The googol (also spelled google) was named by the
nine-year-old nephew of the American mathematician
Edward Kasner.
Write 7.8 × 109 in standard
notation.
What is the value of 100?
Any number to the zero power is
equal to 1.
How can we compare the values 7.034
× 109 and 2.36 × 105 when they are
expressed in scientific notation.
• We can compare the exponents of 10.
• Because 109 has a greater exponent than 105,
7.034 × 109 is greater than 2.36 × 105.
• When comparing two numbers written in
scientific notation, compare the power of 10 first.
• When the power of 10 is the same, compare the
coefficients.
• When the power of 10 is different, you do not
need to compare the coefficient.
Cognitive Strategies
Visualize how the final number will
look before you write anything down.
• If the question says “Write in scientific
notation,” realize that the answer will be the
product of a number greater than or equal to
1 and less than 10, and a power of 10.
• If the question says “Write in standard
notation,” be aware that an answer may have
zeros as placeholders to show the number’s
size.
Which of the following numbers are
written in scientific notation?
• 0.641 x 103
• 9.999 x 104
• 2 x 101
• 4.38 x 510
Which measurement would be
least likely to be written in
scientific notation: number of
stars in a galaxy, number of grains
of sand on a beach, speed of a car,
or population of a country?
Explain your reasoning.
Compare the two numbers to find
which is greater. Explain how you
can compare them without writing
them in standard notation first.
4.5 × 106
2.1 × 108
Exit Ticket
1. The approximate mass of Mars is 6.42 × 1023
kilograms. Write this mass in standard notation.
2. An adult blue whale can eat about 40,000,000
krill a day. Write this number in scientific
notation.
3. Write 9 in scientific notation.
4. Write 1.0 × 105 in standard notation and in
words.
5. Is 10.2 × 105 written in scientific notation?
Explain.