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, thenb 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.

29000 = 2.9*104
Scientific notation is when you have a number between one and ten multiplied by a power of ten to more simply express a large number.

For 29000, one would simply break it up into a power of ten multiplied by a number between one and ten. There are three zeros, meaning one thousand, and one would think that therefore the power of ten would be 103. However, this is not the case. What is left over is 29. 29 is certainly not between 1 and ten. However, 2.9 is. There you simply divided by ten. So you must add another power to your power of ten.

The scientific notation would therefore be :

104 x 2.9.

Some examples of scientific notation:

6,300,000 is 6.3 x 106. .00000000000000524747474 is 5.247 x 10-16 (rounded to 4 significant figures)

0.0000000056, we write 5.6 x 10-9

953 in scientific notation is 9.53 x 10^2