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# Scientific notation examples

Scientific notation is a way of writing very large or very small numbers. A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10. For example, 650,000,000 can be written in scientific notation as 6.5 ✕ 10^8. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• What if it has different exponents ?
• How would you turn a number like this into scientific
notation?:1,300,900,000
the video explains well how to do #'s like 83,000,000 but this was kinda tricky
• You look for the first significant digit (non 0), which is 1 and put a decimal after that, so 1.3009, count how many times you moved the decimal which is 9, so answer is 1.3009 * 10^9.
• so what wouldit be for 0.3643
• 3.643x10^-1 in scientific notation
• I'm very confused. I've watched this video idek how many times and i still don't get it. I need help.
• Continue:
There are also negative powers of 10.
For example, 1.75 x 10^-3.
Using the method mentioned before, you just move the decimal 3 digits to the right. But when there are a lot of zeros, it will be super-confusing.
So here is an easier way:
Because it is 10 to the -3rd power, you just add 3 zeros in front of 1.75.
So it becomes: 000175.
Another example:
Write 0.00281 in regular notation.
First, find the number between 1 and 10: 2.81.
Then, we count the zeros in front of 281 -- there are 3.
So we can know how to write: 2.81 x 10^-3.
It is quite long, but I hope it helps.
• I have a question regarding the last problem
It was 0.000029 X 10^5
wont we write down 0.000029 in scientific notation first which will be 2.9 X 10^-5 and then multiply with 10^5 and then wont the answer be 2.9 and not 2.9 X 10-^5
• Well, what Sal said is that if we want to write 0.000029 in scientific notation we want the coefficient to be 2.9, which we would get by moving the decimal point five steps to the right, and that is equivalent to multiplying by 10⁵.
So, yes, 0.000029 × 10⁵ = 2.9

But our intention was not to change the value of 0.000029, so we can't just multiply by 10⁵, but must also multiply by 10⁻⁵.
So, 0.000029 = 0.000029 × 10⁵ × 10⁻⁵ = 2.9 × 10⁻⁵
• 3400 in scientific notation
• 3400 in scientific notation is equal to 3.4 * 10^3. Hope this helps!
• In the end, Sal said 2.5 instead of 2.9
• does scientific notation ONLY deal with 10?
• Our number system is base 10 (all the place values are powers of 10). This is why scientific notation uses 10s. To use a different value from 10, you would need a number system that has an alternate base.
• so whatever the exponent is that's how many spaces you move to the right/left?
• Yes, move the decimal point when the number 10 is raised exponentially. For example, if you are given 3 times 10 to the 2nd power, written as 3*(10^2), it can be written in standard form as 300. So, when multiplying by 10 raised to the power of a positive whole number, x, move the decimal point x places to right and put in any necessary zeros. This works because:
3*(10^2)=3*(10*10)=3*(100)=300
Likewise, if you have a negative exponent, such as in 3*(10^(-2)), you can think about it as moving the decimal point 2 places to the left and inserting any necessary zeros to show place value. This works because:
3*(10^(-2))=3*(1/(10^(2)))=3*((1/10)*(1/10))=3*(1/100)=3/100=.03
• If you were multiplying 85600000 by 37200000 would you convert both numbers to scientific notation first and then multiply them, or would you multiply them first and then convert the answer to scientific notation?
• I would not convert first.

I would multiply the non-zeroes 856 by 372 to get 318432.

Then add the number of zeroes of both the original numbers
856 00000 and 372 00000

to get
3,184,32 0,000,000,000

then I would convert this to scientific notation as 3.18432 x 10^15

When I get to the point where you add the zeroes I wont actually write them down because at that point you can just write the scientific notation when you get 318432 just remember to count their places they will take (10).