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2.1 Exponents and Scientific Notation
Did you ever take a shortcut when walking from
one place to another? You can also use
shortcuts in math. When you use an exponent,
you are writing a long multiplication problem in
a shortened form.
An ___________________________ tells you how
many times to use the base number as a
factor in a multiplication problem.
There are two parts to a number written in
exponential form:
35
exponent
Base number
This tells you to use the base number, 3, as a factor 5 times =
3 x 3 x 3 x 3 x 3 = _________
The zero (0) power of any number is always
_________.
The first power (1) of any number is
that number.
Prime Factorization
200
Find the prime factorization of 200, in
exponent form:
1) Make a factor tree and factor the number
until you
have all prime numbers: _______________
2) Write the factorization in exponent
form: ________
Scientific Notation
On average, the Earth is 92,900,000 miles
from the sun. It is convenient to write
very large numbers in a shortened form,
called ____________ ________________.
Scientific notation expresses a number as
the product of a decimal number from 1-9 and
a power of 10.
To write numbers in scientific notation:
1)
Remove all the zeroes from the end of the
number: 92,900,000.
2)
Write the remaining digits as a decimal
number from 1-9: 9.29
3)
Count the number of decimal places you
moved back. This will be your power of ten.
92,900,000.
4)
Scientific notation of 92,900,000:
_____________________
Write in scientific notation.
88,900
809,123
Challenge:
340.0200
To write a scientific number in standard form:
1) move the decimal point forward the same number of
spaces as the exponent
2) 2.34 x 107 = move the decimal point forward 7 spaces
and write the new number. Answer: ____________
3)
2.34 x 10-7 = move the decimal point backward 7
spaces and write the new number. _______________
Write in standard form.
1.092 x 104
6 x 10-8
Challenge:
5.6554 x 103