Scientific Notation

Scientific notation is a way of representing numbers, usually very large or very small, in the form

a*10^b where 1<= |a| < 10 is a decimal number and b is an integer (negative or positive).

a is called the mantissa and b is called the exponent.

To convert a number to scientific notation:

• If the number has no decimal point, then add one at the end.
• Then move the decimal point to just after the first digit while counting the number of places you have moved it.
• The new number, formed after moving the decimal point is a.

• If the original number is negative, then so is a.

• The number of places to the left that the decimal point was moved is b. If it was moved to the right, then b is negative.

For example:

23045.06 becomes 2.304506*10^4

-23045.06 becomes -2.304506*10^4

0.00023004 becomes 2.3004*10^(-4)

To convert a number in scientific notation to normal form:

• If b is positive, move the decimal point b places to the right in the number a - adding 0s at the end of the number, if required.
• If b is negative, move the decimal point b places to the left in the number a - adding 0s immediately after the decimal point, if required.
• The final expression has the same sign (+ or -) as a in the scientific form.

For example:

4.56*10^5 = 456000.

-4.56*10^5 = -456000.

4.56*10^(-5) = 0.0000456

I have avoided using the term "Standard form" because, ironically, it is a non-standard term. In the UK Standard and Scientific forms are the same whereas in the US, the Standard form is what I have chosen to call the normal form.

In both notations a number is represented in the form a*10^b where a is a real number and bis an integer.

In scientific notation, 1 <= a < 10 and b is any integer.

In engineering notation, 1 <= a < 1000 and b is a multiple of 3.