Chemistry math scientific notation equations help!

[u/Scared_Mushroom2415]

Hi there, I'm currently doing college level chemistry and it's is asking me to put the numbers (291.7 and 0.096) in to scientific notation. I know you need to move the decimal and I know you need to time it by the amount of time you needed to move the decimal, but when I put those calculations in to my calculator (291.7×10⁴ and 0.0960×10²) I don't get the number I'm looking for. It's supposed to be a big number *as far as I understand* but it's won't come out correctly. Can anyone PLEASE help me I'm literally sobbing over the fact I can't understand...

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[u/spmcn]

It’s pretty simple actually. You move the decimal point until only one digit remains, then multiply by 10 raised to the number of places you moved.

If you moved left, positive exponent. For example:

4,500 = 4.5 x 10^3 (moved 3 places left)

If you moved right, negative exponent. For example:

0.0032 = 3.2 x 10^-3 (moved 3 places right)

Hope that helps!

EDIT: i realize you actually probably understand how to do it but are trying to understand how to do it in a calculator. Usually there’s a setting in your calculator that will convert it for you. Look up a youtube video or just a guide online for your specific calculator.

[u/BornInAWaterMoon]

To start with, you move the decimal until the number you have is between 1 and 10. So in your first example you move the decimal two places to the left so that you have 2.917.

Now notice that what you have done is divide the original number by 100 (which you can write as 10²). So now you need to multiply your 2.917 by that number so that you end up with the same value you started with. So the final result is 2.917 × 10².

The principle is the same for the other number but this time at the start you will be moving the decimal place to the right instead of the left. Give that a try and see what you come up with. You should end up with a negative power of 10 in your final answer.

[u/diverJOQ]

it isn't clear what you're trying to do. Where did the ×10⁴ and ×10² come from?

Scientific notation requires one non-zero digit to the left of the decimal point.

Need on your original numbers:

291.7 : since you have to move the decimal point two places to the left to get 2.917 you've made the number smaller so you have to multiply it by 10 to a positive power and that power is the number of locations that you move the decimal point, so 2.

291.7 = 2.917 × 10²

0.096 : here you are moving the decimal point to the right, making the digits a larger number (9.6) so the exponent that you use has to be a negative number. Since the decimal point was again moved to two places the exponent will be -2.

0.096 = 9.6 × 10-² (that should be 10 raised to the negative 2 power)

[u/StructuredChess]

Not exactly sure what you're inputting on your calculator..

Start with 0.096, that's the same as 0.096 * 10⁰. Move the decimal point once, now you have 0.96 * 10^-1. Move it again and that's 9.6 * 10^-2. Now you have a single non-zero digit before the deciaml point, so you're done.

Same goes the other way around. let's say you have 4206.9, that's 4206..9 * 10⁰. Instead of one by one I'll move the dot three spaces together to get 4.2069 * 10³

If you want to check if your calculation was correct and can't seem to figure out how to do it on the calculator, just google 4.2069 * 10^3 - 4206.9. If you get 0, you did it right.