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### Course: Pre-algebra>Unit 11

Lesson 6: Scientific notation intro

# Scientific notation review

Review the basics of scientific notation and try some practice problems.

## Scientific notation

A number is written in scientific notation when there is a number greater than or equal to $1$ but less than $10$ multiplied by a power of $10$.
The following numbers are written in scientific notation:
• $5.4×{10}^{3}$
• $8.013×{10}^{-6}$

## Writing numbers in scientific notation

### Numbers greater than $10$‍

If we have a number greater than $10$, we move the decimal point to the left until we have a number between $1$ and $10$. Then, we count the number of times we moved the decimal and write that as an exponent over a base of $10$. Finally, we write our number multiplied by the power of $10$.
Example
Let's write $604,000$ in scientific notation.
If we move the decimal left once, we get $60,400.0$. We need to keep moving the decimal until we get a number between $1$ and $10$.
We have to move the decimal left a total of $5$ times.
Now, we have $6.04$.
Finally, we multiply $6.04$ times ${10}^{5}$:
$604,000$ in scientific notation is $6.04×{10}^{5}$.

### Numbers less than $1$‍

If we have a number less than $1$, we move the decimal point to the right until we have a number between $1$ and $10$. Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of $10$. Finally, we write our number multiplied by the power of $10$.
Example
Let's write $0.0058$ in scientific notation.
If we move the decimal right $3$ times, we get a number between $1$ and $10$.
Now, we have $5.8$.
Finally, we write $5.8$ times ${10}^{-3}$:
$0.0058$ in scientific notation is $5.8×{10}^{-3}$.

## Practice

Problem 1
Express this number in scientific notation.
$245,600,000,000$

Want to try more problems like this? Check out this exercise.

## Want to join the conversation?

• I get confused on which way I should move the decimal for each exponent. Does anyone Have a trick or saying that helps them remember this.
Thanks.
• A positive exponent means move to the right, and a negative exponent means move to the left.
• I don't understand this concept. Would someone explain a scientific notation problem for me? I'm not trying to sound "witty and intelligent" as EAP said down there. I'm actually struggling. Please help me with this concept so I don't get summer slide...
• Scientific notation is simple. You use it when there is a very big number that is too hard to read, so you make it shorter. Let's take 0.00014, you have to move the decimal to the right until you get a number that is between 1 and 10. You get 1.4, so you count how many spaces you moved to the right. If you count, you moved 4 to the right, so the base will be 1.4 and the exponent will be -4. The reason why it is a negative is because when moving to the right, it is negative, and moving left, it's positive. So the full statement will be 1.4 x 10 to the power of -4.

Now, let's take 12000000. You have to move to the left this time. You might not see the decimal, but it comes after the last zero. You move that invisible decimal to the left, and you move it 7 to the left. This makes the exponent positive, so it is 1.2 x 10 to the power of 7.

Note: You must always use 10.
• This is so hard how do you know neg and pos
• If your original number in standard form is a large number, then you get a positive exponents.
For example: 5,000,000 = 5 x 10^6

If your original number in standard form was a decimal, then you would have a negative exponent.
For example: 0.00006 = 6 x 10^(-5)

Hope this helps.
• why did people make scientific notation?
• In order to simplify numbers that are to big
• This is so dumb, I´m giving the right answer but khan is not grading it correct because I didn´t do it their way

does anyone else have the same problem?
• How do you get it wrong with the right answer, regardless of your working out? Khan Academy doesn't look at how you worked it out.

For the multiplication symbol, did you perhaps write x instead of *? The system treats x as the letter variable.
• How do negative numbers in scientific notation work? (34*10 to the negative 6th power)
(1 vote)
• When you have dissimilar exponent, when doing addition and subtraction, what rule is used to determine which side gets adjusted? For instance,
1.7*10^-4 + 3.5*10^-3
. Which side of the equation do you adjust, the -4 or the -3 side?
• Both sides would work, as long as you factor out the power of ten, and then add and convert properly.
• i got a question that connects to this is can i add a negative notation to a positive notation
• What are the advantages of using scientific notation when dealing with very large or very small numbers?
(1 vote)
• Scientific notation ("standard form" for British English speakers) lets us condense a number. Writing the power that a number is raised to saves us a lot of space by omitting zeroes more often than not. The biggest advantage, though, is that it allows us to get a scale of the number very easily. If for example, we know that a billion has nine zeroes, we can easily understand how big or small this number is:
7.8 x 10^9
you immediately understand that this is 7.8 billion, and
this:
8 x 10^-9
is eight billionths.
It gets more useful the larger a number gets.