# Using scientific notation on my retirement account (which might be in the ten-thousands) could be over simplifying and a lot of data could be lost; for example, say I have \$65,493 saved for...

Using scientific notation on my retirement account (which might be in the ten-thousands) could be over simplifying and a lot of data could be lost; for example, say I have \$65,493 saved for retirement, I would lose a lot of data if I say 6.5X10^4 but when dealing with trillions of dollars are you really losing anything if you are off by a few million?

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

Scientific notation is NOT ideal for expressing monetary values and is more valuable in chemistry and statistics.

When you use scientific notation, you are not required to round off to only one decimal so \$65,493 could be written as 6.5493 x 10`^(-4)` .Note it is a negative exponent.

It is when you are dealing with scientific notation and significant figures that you may be restricted in how you round off. When considering the speed of light, for example,

light travels such a large distance in 10 years that even an answer in terms of billions of kilometers would suffice, just using 3*10^8 is enough.

The rules of scientific notation are

• only one number greater than zero (ie 1. or 2. or 3. up to 9.)
• If you make the number smaller (ie the decimal is moved to the left eg 65 493 becomes 6.5493 x 10 `^(-4)` ) the exponent is negative
• If you make the number bigger (ie the decimal is moved to the right eg. 0.054 becomes 5.4 x  10 `^2` ) the exponent is positive.

Therefore scientific notation can be rounded off to fewer significant figures for some purposes - money would not be one of them. Compromising a monetary value with millions or trillions could be very costly.

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