Describe Number Naturally

Question

I'm running some calculations on a calculator, and I'm getting a lot of "exponent of 10" results. I was hoping somebody could help me translate the results to a "normal" representation, so that I can better understand what is going on.

For example, 3.772819472616633e-4 would become, I imagine, something like 0.000000...? Am I mistaken?

I would like write each of the following numbers without the 'exponent of 10' notation, but I'm not sure how to do that.

3.772819472616633e-4
1.476959432847578e-4‬
2.434077079107505e-5

P.S. If my tags are the wrong ones, please adjust them. Thanks.

Answer 1

Treat the $+$ or $-$ sign like the direction on the number line ($+$ is right and $-$ is left).

Move the decimal point the number of spaces in the direction indicated:

• $1.23\text{e-2} = 0.0123$
• $1.23\text{e+2} = 123$
• $1.234567\text{e+10} = 12345670000$
• $1.234567\text{e-10} = 0.0000000001234567$

Answer 2

The "e-4" you see just means $\times 10^{-4}$. Similarly a "e+4" would mean $\times 10^4$.

For example: $1.23 \text{e-4} = 0.000123$, and $1.23 \text{e+4} = 12300$.