Sales Toll Free No: 1-800-481-2338

# Scientific Notation and Rational Numbers

Top

A rational number is a number which can be expressed exactly as a fraction $\frac{p}{q}$ where p and q are two integers with denominator non zero and represented by 'Q'. The addition and multiplication operations together form a field. Rational Numbers are the smallest field with characteristic zero, it means every other field of characteristic zero contains a copy of 'Q'.

Now the scientific notation is defined as a standard way of writing very large or very small numbers so that they are easier to compare and use in computations.

The standard form of scientific notation is given as: N $\times$ 10a

where 'N' is a number between 1 and 10, but not 10 itself, and 'a' is an Integer number.

We move the decimal Point of a number until the new form, and then record the exponent (a) as the number of places the decimal point was moved. Whether we move the decimal to right or to left then the power of 10 is positive or negative depends on it. Moving the decimal to the right makes the exponent negative, moving it to the left gives you a positive exponent.

For example: Let us write 622,000,000,000 in scientific notation

Step 1: Move the decimal place to the left.

For example, we write 622,000,000,000 in decimal. The decimal point is placed at the end of the number 622,000,000,000 and written as:

N = 6.22

Step 2: Now, determine how many times we moved the decimal. In this example, we moved the decimal 11 times and as the exponent is positive, in this we also move the decimal to left. Therefore, a = 11, and so we get 1011.

Step 3: Lastly, put the number in the correct form of scientific notation that is, N x 10a,

$\therefore$ 622,000,000,000 = 6.22 x 1011.

In this way, we write the scientific notation of any number.