Have you ever noticed that 450 could be written
as 45 x 10 or that 450 could be written as 4.5 x 100
(check this with your calculator) What could 5,6784
be written as answers
Could 4.5 x 100 in the above example be written
as 4.5 x 102? Use your calculator to check the answer.
4500 = 4.5 x 103
45000 = 4.5 x 104
4500000 = 4.5 x 106
The three above problems are in scientific notation
The distance from the earth to the sun is approximately
93,000,000 miles. This number could be written
as 9.3 x 10,000,000. It could also be written
as 9.3 x 107. In this form it is called Scientific Notation.
In scientific notation numbers are written so that there
is 1 digit (never would this digit be zero) to the left of
the decimal point and the resulting number is multiplied
by a power of ten expressed by using 10 and an
exponent. How do we determine the exponent?
Look again at 93,000,000 and remember that all whole
numbers have a unwritten decimal point to the right
of the last digit. For example 567 could be written
as 567. but we don't write the decimal point. How
many places have we moved the decimal point to
change from 93,000,000 to scientific notation and
what is the exponent? answer
Try these examples -
change 47,000 to scientific notation
change 506,000 to scientific notation
change 3.546 x 106 back from scientific numbers answer
Using scientific notation with decimal numbers.
0.0000067 written in scientific notation is 6.7 x 10-6
Count the number of places we have moved the
decimal point and notice that we are using a
negative exponent. The negative exponent tells
us that we moved the decimal point to the right.
Again we have one digits to the left of the
decimal point and that digit is never zero.