How would you define scientific notation?

Answer 1

Scientific notation is used to express [very] large and [very] small numbers.

By using scientific notation very large and very small numbers are written in a compact and easy to read form.

To convert a number from standard form to scientific notation:

1) Write the number by writing the first non-zero digit followed by a decimal point

2) write the rest of the digits of the number stopping after the last non-zero digit of the number.

3) write "×10"

4) Now write a power for the 10. To work out the power count the number of digits the decimal point needs to move to get back to where it was in the original number (if there is no decimal point in the number it is "hiding" after the last digit of the number). If this movement is to the right leave it positive, otherwise if the movement is to the left make it negative. If the decimal point does not need to move, the power is 0.

examples:

123000 = 1.23×10^5

0.00123 = 1.23×10^-3

1.23 = 1.23×10^0

0.0120 = 1.2×10^-2

Answer 2

Scientific notation is a way to express numbers that are either very small or very large. In traditional notation the first kind would have a lot of 0s between the decimal point and the first significant digit whereas the second kind would have a large number of trailing 0s. The need for scientific notation arose from advances in various branches of science: atomic particles in physics or chemistry, astronomical or cosmological distances, size of single cell animals. Nowadays, even non-scientific values such as population, national debts (of some countries) could usefully utilize scientific notation.

In scientific notation a number is represented as a*10^b where 1 <= |a| < 10 is a decimal number and b is an integer (negative or positive). ais 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 mantissa of 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