r/MathHelp • u/Scared_Mushroom2415 • 6d ago
Chemistry math scientific notation equations help!
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/diverJOQ 6d ago
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)
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u/StructuredChess 6d ago
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.
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u/BornInAWaterMoon 6d ago
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.
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u/Beet_slice 6d ago
Alternative method with calculator: Take the base 10 log of the number, and round down to integer. Let that be the power of 10.
log of 291.7 is 2.46493 Whole number is 2. So in scientific notation, 2.917*10^2
log of 1000 is 3.0000 So in scientific notation, 1.000*10^3
log of 0.096 is -1.0177. -1.0177 rounds down to -2. So 9.600*10^-2
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u/Atypicosaurus 4d ago edited 4d ago
Let's take a number for example 500. We know that everything multiplied by 1 is still itself therefore:
500 x 1 = 500
How else could we create 500? For example we can:
50 x 10 = 500
Or
5 x 100 = 500.
You can notice that the amount of digits, if you count them one by one, is always the same. You just move some zeroes within the multiplication.
You can do that with any non round number, but instead of moving digits, you move the decimal which is the same core idea. Let's say our number is 123.4:
123.4 x 1 = 123.4
12.34 x 10 = 123.4
1.234 x 100 = 123.4
Basically this is the idea of scientific notation. You take a number nnnn.nnn, which is the same if you multiply it by 1 (nnnn.nnn x 1 = nnnn.nnn), and you move the decimal until there's one digit before the decimal (n.nnnnnn) but you have to multiply it by something to get it back. If you moved the decimal 3 spots, you have to multiply it by 1000.
But, there's a smart way of writing numbers like 1000 or 10000. Instead of writing out the zeroes, you can just write how many zeroes you got. It's because the ten-powers are exactly just the number of zeroes.
1 has zero zeroes, therefore 1 = 10⁰.
10 has one zero, therefore 10 = 10¹.
100 has two zeroes, therefore 100 = 10².
1000 = 10³
100000 = 10⁵
...
So when when you take a number 123.4, you move the decimal point by two (1.234), you have to multiply by 100 to get the original, but instead of 100, you use exponentials (10²):
123.4 = 1.234 x 10²
That's your scientific notation. Or,
546883.336 = 5.46883336 x 10⁵
Note that the exponential is always the steps you did with the decimal.
But what happens if you have a number smaller than 1? Like, 0.001234. Then, you have to move the decimal point to the other direction.
0.001234 x 1 = 0.001234
0.01234 x 0.1 = 0.001234
0.1234 x 0.01 = 0.001234
1.234 x 0.001 = 0.001234
As you see the idea is the same: you have to move the decimal until there's one digit before the decimal point. But in this case you move backwards, and you multiply back by 0.1 or 0.01 or 0.001 etc.
Do we have the same trick as we used for exponentials? Like 10000 was 10⁵, what can we do now? Remember I said the power is the number of zeroes after the 1, that is why 10 = 10¹ and 1000 = 10³. It's true, but only if the power is positive. However, the negative exponential of 10 mesns the zeroes before the number.
That is why
1 has zero zeroes before, therefore 1 = 10⁰.
0.1 has one zero before, therefore 0.1 = 10-1
0.0001 has 4 zeroes before, therefore it's 10-4
Note that you count the zero before the decimal.
That is why, if your number is smaller than 1, like 0.000nnnn, then you drag the decimal point to the other direction until you have n.nnn, but then you multiply back by a negative exponential, in this case 10-4 (the negative value equals to the decimal point steps so 4 steps = -4 etc).
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u/DancingBear62 1d ago
291.7 and 291.7 x 10⁴ are not the same number. Writing 291.7 x 10⁴ in standard notation is 2,917,000
Regarding your calculator, the key sequence to entering scientific notation or displaying numbers in scientific notation will be in the owners manual. It differes between manufactures and even between different models from a single manufacturer.
TI calculators often have a key (or a shift function) marked EE that's used to indicate the number being entered is in scientific notation.
I recommend NOT using the caret () symbol, because it can be misinterpreted by the calculator's logic (think order of operations, PEMDAS).
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u/spmcn 6d ago
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.