Scientific Notation
7
The number 3 5 x 10
6 might equally well be written as 35 x 10
5 , 350 x 10
4 , or
0 35 x 10
7 , and so on All of these forms are equivalent, for each calculation, we
could arbitrarily set the decimal point at the most convenient place However,
the convention is to leave the lefthand number in the range between 1 and
10—that is, with a single digit before the decimal point This form is known as
standard scientific notation
PROBLEM:
Write the number 0 00055 in standard scientific notation
SOLUTION:
We want to set the decimal point after the first 5 as indicated by the small v
0 0005 X 5
Because we are thus moving the decimal point four places to the right we must
decrease the exponent on the 10° by 4 Therefore the scientific notation is 5 5 x
io4
You must be able to enter numbers easily and unerringly into your calculator
using scientific notation With most calculators, this would be accomplished as
follows.
1 Write the number in standard scientific notation Standard notation
isn't required, but it is a good habit to acquire
2 Enter the lefthand factor through the keyboard
3 Press the exponent key (common key symbols are EEX and EE)
4 Enter the exponent of 10 through the keyboard If the exponent is
negative, also press the "change sign" key (common symbols are CHS
and +/ —) It is important that you don t press the - key (i e , the
subtract key)
5 The lefthand factor of the desired scientific notation will occupy the
lefthand side of the lighted display, while the three spaces at the righthand end of the display will show the exponent (a blank space followed
by two digits for a positive exponent, or a minus sign followed by two
digits for a negative exponent If the exponent is less than 10, the first
digit will be a 0—for example, 03 for 3)
Some calculators make it possible for you to choose in advance that all
results be displayed in scientific notation (or decimal notation), regardless of
which notation you use for entering numbers You can also choose how many
decimal places (usually up to a maximum of 8) will be displayed in decimal
notation, or in the lefthand factor of scientific notation If your calculator has
7
The number 3 5 x 10
6 might equally well be written as 35 x 10
5 , 350 x 10
4 , or
0 35 x 10
7 , and so on All of these forms are equivalent, for each calculation, we
could arbitrarily set the decimal point at the most convenient place However,
the convention is to leave the lefthand number in the range between 1 and
10—that is, with a single digit before the decimal point This form is known as
standard scientific notation
PROBLEM:
Write the number 0 00055 in standard scientific notation
SOLUTION:
We want to set the decimal point after the first 5 as indicated by the small v
0 0005 X 5
Because we are thus moving the decimal point four places to the right we must
decrease the exponent on the 10° by 4 Therefore the scientific notation is 5 5 x
io4
You must be able to enter numbers easily and unerringly into your calculator
using scientific notation With most calculators, this would be accomplished as
follows.
1 Write the number in standard scientific notation Standard notation
isn't required, but it is a good habit to acquire
2 Enter the lefthand factor through the keyboard
3 Press the exponent key (common key symbols are EEX and EE)
4 Enter the exponent of 10 through the keyboard If the exponent is
negative, also press the "change sign" key (common symbols are CHS
and +/ —) It is important that you don t press the - key (i e , the
subtract key)
5 The lefthand factor of the desired scientific notation will occupy the
lefthand side of the lighted display, while the three spaces at the righthand end of the display will show the exponent (a blank space followed
by two digits for a positive exponent, or a minus sign followed by two
digits for a negative exponent If the exponent is less than 10, the first
digit will be a 0—for example, 03 for 3)
Some calculators make it possible for you to choose in advance that all
results be displayed in scientific notation (or decimal notation), regardless of
which notation you use for entering numbers You can also choose how many
decimal places (usually up to a maximum of 8) will be displayed in decimal
notation, or in the lefthand factor of scientific notation If your calculator has