Welcome to scientific notation. How can I convert a number larger than one to scientific notation?
Below you see both large ordinary numbers and numbers written in scientific notation.
The approximate distance that light travels in one year, called a light year,
is 9 quadrillion 450 trillion meters. The student pictured below has three thoughts;
that large number is very difficult to read and very inconvenient to write, expressing it
in scientific notation would be much simpler, how can I convert it to scientific notation?
To convert a number larger than one to scientific notation follow these three steps. Step one:
move the decimal point so that one and only one non-zero digit
is to the left of the decimal point, drop all unnecessary zeros.
Step two: count the number of places you would have to move the decimal point
to get it back to its original position. That number is the power or exponent of 10.
Since you have to move the decimal point to the right (which is the positive direction on
a number line) to get it back to its original position, the power of 10 will be positive.
Step 3: write a multiplication problem with a new decimal number from step 1 being
multiplied by the power of ten from step two. For example let's go back to that large number
that represents the approximate distance light travels in one year, a light year.
Step one: move the decimal point so that one and only one non-zero digit is to the left of
the decimal point, drop all unnecessary zeros. This gives us 9.452. Count the number of places
you would have to move the decimal point to get back to its original position. That
number is the power or exponent of ten. Since you have to move the decimal point to the right
(which is the positive direction on a number line) to get back to its original position,
the power of 10 will be positive. We count 15. This means 10 to the 15th power.
Step three: write a multiplication problem with the new decimal number from step one
being multiplied by the power of ten from step two.
9.45 from step one times 10 to the fifteenth power from step two.
Now try these.
Congratulations! You've completed converting large numbers to scientific
notation.