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### Course: 8th grade>Unit 1

Lesson 10: 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:
• $5.4×{10}^{3}$
• $8.013×{10}^{-6}$
Want to learn more about scientific notation? Check out this video.

## 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.
(43 votes)
• A positive exponent means move to the right, and a negative exponent means move to the left.
(27 votes)
• Is this for seventh graders?
(17 votes)
• You Learn maybe before 8th grade, but you learn around 8th grade (or pre-algebra at OLP)
(13 votes)
• Is it possible for a number to have an infinite answer?
(16 votes)
• Yes, for example, x(2+3) = 2x+3x, once you simplify the first expression you get 2x+3x = 2x+3x, which means it has infinite solutions.
(17 votes)
• when am i gonna do this when im older
(11 votes)
• imagine ur boss at the math-a-matical company earns alot of money. ur his secretary. and he wants u to keep check of how much money he has, but in a shorter, more organised form. scientific notation might be the way to go. otherwise this isnt very helpful :/
(22 votes)
• i was stuck on this for the longest time just because i kept forgetting about the decimal point.
(15 votes)
• is it possible to have a negative pi
(6 votes)
• Every real number has an opposite, so negative pi exists.
(15 votes)
• This is so hard how do you know neg and pos
(6 votes)
• 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.
(12 votes)
• 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...
(10 votes)
• 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.
(3 votes)
• why are there negative exponents
(6 votes)
• Negative exponents represent inverses of repeated multiplication; in other words, the value of the base not only wasn't able to get a repeated multiplication produced, it had to give something up before the exponent would be satisfied.
(8 votes)
• How do you write scientific notation in standard form? I still don't get it even after watching the videos.
(5 votes)
• for writing scientific notation in standard form we have to remove 10 exponent ; if exponent is in negative then we have to move decimal to left;{ 5.4*10^-1= 0.54} and if power of exponent is positive then we move decimal to right{ 2.456 *10^2= 245.6} hope it helps
(4 votes)