# 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?

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### 1 Answer

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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