The method of writing extremely large or small numbers in science is known as scientific notation. Numbers in scientific notation are made up of three parts. The coefficient, the base and the exponent.
There are a few rules followed in scientific notation:
Rule 1: Writing a number in scientific notation involves expressing it as a product of a number between 1 and 10 and a power of 10. If the original number is larger than 1, the power of 10 will be positive, and if it is smaller than 1, the power of 10 will be negative.
Rule 2: The power of 10 in scientific notation indicates the number of times you need to move the decimal point to the right (if it’s positive) or to the left (if it’s negative) to get the original number.
Rule 3: The scientific notation form should have only one non-zero digit to the left of the decimal point. This digit is called the coefficient or mantissa.
Example 1:
Express 72,000 in scientific notation.
Step 1: Move the decimal point until you have one non-zero digit to the left of it: 7.2
Step 2: Count the number of places you moved the decimal point: 4 places to the right.
Step 3: Write the number in scientific notation: 7.2 x 104
Example 2:
Express 0.00025 in scientific notation.
Step 1: Move the decimal point until you have one non-zero digit to the left of it: 2.5
Step 2: Count the number of places you moved the decimal point: 4 places to the left.
Step 3: Write the number in scientific notation: 2.5 x 10-4
Example 3:
Express the speed of light, which is approximately 299,792,458.00 meters per second, in scientific notation.
Step 1: Move the decimal point until you have one non-zero digit to the left of it: 2.99792458
Step 2: Count the number of places you moved the decimal point: 8 places to the right.
Step 3: Write the number in scientific notation: 2.99792458 x 108 meters per second.
Remember, scientific notation makes it easier to work with very large or very small numbers in physics and other scientific disciplines.