Mr. Manzo - Regents Earth Science
How to Use Scientific Notation
Background Information:
Many times in science, we deal with very large numbers or extremely small numbers. Using scientific
notation (using a power of 10 base scale) is a way to express these values in a shortened format for easier
analysis. Some examples are given below:
Very Large Numbers:
1. The speed of light is 300,000,000 m/sec. To write this in scientific notation, a decimal is placed
after the first NON-ZERO number. In this case, it is a 3. Scientific notation involves a
coefficient and an exponent for the 10. Therefore, this number is written as:
3.0 x 108
The 3.0 is the coefficient. Notice that the exponent is simply the number of places the decimal
was moved to the LEFT to place it after the first NON-ZERO number (the 3 in this case).
2. In the case where other non-zero digits appear in the number, they must be included as part the
coefficient. For example, the diameter of the Sun is 1,392,000 KM. This number is written in
scientific notation as:
1.392 x 106
In this case, ALL NON-ZERO digits must be included in the coefficient. The
exponent on the 10 is still the number of places the decimal had to be moved to put it after the first
non-zero digit.
Very Small Numbers
3. The estimated mass of a dust particle is 0.000000000753 kg! Using commas to help organize this
number, we have 0.000,000,000,753. Numbers less than 1 will have a negative exponent when
written in scientific notation. The coefficient is still ALL NON-ZERO digits, with the decimal
placed after the first non-zero digit, in this case the 7. The exponent is the number of places to the
right the decimal must be moved to place it after the first non-zero digit. Therefore, this number is
written as:
7.53 x 10-10
4. For one final example, we will take a really small number out of scientific notation. The number
8.0942 x 10-6 is the correct scientific notation for the following number: 0.0000080942
Notice that the decimal was moved to the left SIX times when writing out the number to account
for the -6 exponent. That means once to move it to the left of the 8, and another 5 zeroes were
added to allow us to move the decimal six times.
HOPE THIS INFORMATION HELPS YOU USE SCIENTIFIC NOTATION IN SCIENCE!!!