Scientific Notation worksheets here teach you the best way to express very lage numbers and very small numbers. It is represented conveniently using exponents. The numbers are shortened (a number between 1 to 10) and multiplied in the power of 10. The powers for very large numbers are expressed using positive exponents and very small numbers using negative exponents. In these worksheets, learn to express standard numbers in scientific form and scientific numbers in standard form. Also scientific notation Addition, Subtraction, Multiplication, and Division worksheets have been prepared for advanced learning.
Let us learn how to express the numbers
The mass of earth is 5,970,000,000,000,000,000,000,000 kg. Such large numbers are represented using exponents. We represent it as 5.97 x 1024
Thus 10 is base here and 24 is the power in 5.97 x 1024
Lets us see how to represent it. Look into the number.
Place a decimal point at the end of the number. Now move the decimal 24 places to the left, such that you place the decimal point imediately after the first digit of the given number.
What does this expression 5.97 x 1024 mean?
5.97 x 1000000000000000000000000 (24 zeros)
5.97 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10.
Eg. Negative Integer
The size of a atom is 0.0000000008 m. We represent it as 8 x 10-10 m. Here you need to move the decimal point10 places right.
What does the expression 8 x 10-10 mean?
8 x 0.0000000001
8 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1
As the exponent decreases by 1, the value becomes one- tenth of the previous value.
Generally mathematicians, scientists and engineers deal with very large and very small numbers on daily basis. They also do exponent addition, subtraction, multiplication, and division. Here is an example for each operation.
When you add two or more exponents, the powers should be made equal first. Its is always better to convert the smaller power to the highest power.
Just like addition, when you subtract exponents, the powers should be the same.
When you multiply two exponents, just add the powers. am x an = am+n, where m and n are natural numbers.
When you divide two exponents, subtract the powers. am/ an = am-n, where m and n are natural numbers.