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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. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

• Does the Scientific notation always have to have a whole lot of zeros!
• sometimes yes but not always, that's the way it is "a way of simplifying or expanding numbers"
• Why does the scientifically notified number have to be below 10?
• Because we can easily understand that 1 is much less than 9 and 4 is about 5, etc. We're familiar with numbers less than 10.

So we can see that 9 * 10^5 is close to 8 * 10^5 but is quite big compared to 2 * 10^5.

It's very similar to place value. 9 tens is quite big compared to 2 tens but is about 8 tens.

Also we understand that 3 * 10^7 is 100 times bigger than 3 * 10^5.
Is it clearer now?
• At (expressing 0.000000027 in scientific form), couldn't 27 x 10^-9 work too?
• Yes, it would work too... but the "rules" or conventions of scientific notation say that the "number" part of it should be less than 10 and the rest as powers of 10. The one you talked about is called the engineering notation, because the power of 10 is a multiple of 3. Such numbers have "names" like millimeters, micrometers, etc. For e.g., `0.000000027 meters = 27 * 10^-9 meters = 27 nanometers`.
• What if it has different exponents ?
• so basically. this is just describing a longer number. but in smaller numbers?
• Yes, because scientific notation is used to express REALLY big numbers or REALLY small numbers. For example, to write out 230000000000, wouldn't you raher go 2.3*10^10 instead of writing it all out? Hope this helps!
• can a whole number be Scientific notated
• Yes. For example if we want to express 5 in Scientific notation we write is as:
5 * 10^0
Since 10^0 = 1 it's the same thing as 5 * 1
And 5 * 1 is just 5.
• 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.
• 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.
• 10 to the power 1 is ten why in this case do you have to put 10 to the power 1