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.
• 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

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.

For example:

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.

Start with 23500000 or 23,500,000.0

See the decimal point? Move the decimal point to the left until there's only ONE number to the left of it.

Count the number of times the decimal is moved to the left:

23,500,00.0 (1 move)

23,500,0.00 (2 moves)

23,500.000 (3 moves)

23,50.0000 (4 moves)

235.00000 (5 moves)

23.500000 (6 moves)

2.3500000 (7 moves)

The decimal point was moved 7 places to the left, so your new answer is the "number" part (2.35) multiplied by 10 to the 7th power, or:

2.35 x 107

Really big numbers have a positive exponent at the end

Really small numbers have a negative exponent at the end