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Course: MAP Recommended Practice > Unit 19
Lesson 6: Scientific notation introScientific 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 but less than multiplied by a power of .
The following numbers are written in scientific notation:
Want to learn more about scientific notation? Check out this video.
Writing numbers in scientific notation
Numbers greater than
If we have a number greater than , we move the decimal point to the left until we have a number between and . Then, we count the number of times we moved the decimal and write that as an exponent over a base of . Finally, we write our number multiplied by the power of .
Example
Let's write in scientific notation.
If we move the decimal left once, we get . We need to keep moving the decimal until we get a number between and .
We have to move the decimal left a total of times.
Now, we have .
Finally, we multiply times :
Numbers less than
If we have a number less than , we move the decimal point to the right until we have a number between and . Then, we count the number of times we moved the decimal and write that as a negative exponent over a base of . Finally, we write our number multiplied by the power of .
Example
Let's write in scientific notation.
If we move the decimal right times, we get a number between and .
Now, we have .
Finally, we write times :
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.(50 votes)- A positive exponent means move to the right, and a negative exponent means move to the left.(36 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...(12 votes)
- I could help you with that. :)(4 votes)
- This is so hard how do you know neg and pos(8 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.(15 votes)
- why did people make scientific notation?(1 vote)
- In order to simplify numbers that are to big(10 votes)
- When you have dissimilar exponent, when doing addition and subtraction, what rule is used to determine which side gets adjusted? For instance,
. Which side of the equation do you adjust, the -4 or the -3 side?1.7*10^-4 + 3.5*10^-3
(2 votes)- Both sides would work, as long as you factor out the power of ten, and then add and convert properly.(5 votes)
- i got a question that connects to this is can i add a negative notation to a positive notation(3 votes)
- How do negative numbers in scientific notation work? (34*10 to the negative 6th power)(1 vote)
- x to the negative y =
1/x^y
So for example, 10 to the negative two would be 0.01 since it's 1/100
More info here: https://www.khanacademy.org/math/pre-algebra/pre-algebra-exponents-radicals/pre-algebra-negative-exponents/v/negative-exponents(4 votes)
- What if its already between 1 and 10?(1 vote)
- Well, if the number is already in between 1 and 10, there's no need to simplify it, because that's a fairly simple number compared to things like 148,000,000 and 0.0000000148- hope this helps! -Your trusty 9th grade homie(3 votes)
- Is there negative scientific notation? It says that it has to be more/equal to one and less than 10. Would it be like this?
-3 * 10^3
=
-3000(1 vote)- Yes, you can do that. For some reason, positive numbers are generally used when doing scientific notation. But, they can be negative. The important thing is that the number before the "times 10s" should have only 1 digit on the left of the decimal point and the digit can't be a zero.(4 votes)
- Wow, I actually get this now.(2 votes)