Scientific Notation
To write a number in scientific notation is simple. Locate the decimal in the number and move it so that only one digit in the number is to the left of the decimal. Next count how many place values the decimal was moved. It is necessary to replace those place values that were removed by powers of 10 where 10 is the base and the exponent is represented by counting how many place values were removed. If the decimal was moved to the left, then the exponent is positive; if the decimal was moved to the right, then the exponent is negative.
Rewrite the number as
3.400. Notice that the decimal was moved 3 place values to the left, so
the exponent would be +3. To replace those place values (powers of 10)
so that the new number is equivalent to 3400, it would be necessary to
multiply 3.4 by1000 or 10
Rewrite the number as
6.78. Notice that the decimal was moved 6 place values to the right, so
the exponent would be -6. To replace those place values (powers of 10)
so that the new number is equivalent to 0.00000678, it would be
necessary to multiply 6.78 by 10
.00000678
= 6.78
x 10
Changing a number from
^{8} in decimal notation. Think of this as
making the number larger (since the exponent is positive) by replacing
(moving the decimal to the right) 8 place values of 10 to the number5.607 x 10 ^{8} = 560,700,000.Notice (above) that 5 zeroes needed to be added to the end of the number since there were only 3 digits to the right of the decimal in the scientific notation number.
^{-5} in decimal notation. Think of this as
making the number smaller (since the exponent is negative) by removing
(moving the decimal to the left) 5 place values of 10 to the number.
8.092
x 10 The views and
opinions expressed in this page are strictly those of Mary Lou Baker. This page was edited on 28-Jan-2013 |