What does a variable mean in scientific notation?

Answer 1

Scientific notation is particularly useful for numbers that are very big (eg 465 000 000 000) or very small (eg 0.000 000 003 98) because it saves you from having to write a lot of zeros. It also gives you a better feel for the magnitude of the number.

The big number above is 4.65 multiplied by 100 000 000 000. The big number to the left is a one followed by 11 zeros, and it can be written as 1011 (ten to the power of eleven). Hence the complete number is 4.65 x 1011 (4.65 times 10 to the power of 11).

Likewise, the small number above is the same as 3.98 divided by 1 000 000 000 (9 zeros), or 3.98 multiplied by 0.000 000 001.

This can be written as 3.98 x 10-9 (4.65 times 10 to the power of -9).

So the scientific notation for the two numbers is 4.65 x 1011 and 3.98 x 10-9.

Scientific notation saves you from having to count a lot of zeros, and avoids errors. Note that I have made the original numbers a bit easier to read by inserting a space between each group of three digits.

If you are happy with scientific notation, you might want to consider a variation on the system, called engineering notation.