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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, point, 4, times, 10, cubed
• 8, point, 013, times, 10, start superscript, minus, 6, end superscript

Writing numbers in scientific notation

Numbers greater than $10$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, comma, 000 in scientific notation.
If we move the decimal left once, we get 60, comma, 400, point, 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 start color #a75a05, 5, end color #a75a05 times.
Now, we have 6, point, 04.
Finally, we multiply 6, point, 04 times 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript:
604, comma, 000 in scientific notation is 6, point, 04, times, 10, start superscript, start color #a75a05, 5, end color #a75a05, end superscript.

Numbers less than $1$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, point, 0058 in scientific notation.
If we move the decimal right start color #1fab54, 3, end color #1fab54 times, we get a number between 1 and 10.
Now, we have 5, point, 8.
Finally, we write 5, point, 8 times 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript:
0, point, 0058 in scientific notation is 5, point, 8, times, 10, start superscript, start color #1fab54, minus, 3, end color #1fab54, end superscript.

Practice

Problem 1
Express this number in scientific notation.
245, comma, 600, comma, 000, comma, 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.
• Is this for seventh graders?
• You Learn maybe before 8th grade, but you learn around 8th grade (or pre-algebra at OLP)
• Is it possible for a number to have an infinite answer?
• 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.
• is it possible to have a negative pi
• Every real number has an opposite, so negative pi exists.
• 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.
• How do you write scientific notation in standard form? I still don't get it even after watching the videos.
• 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
• why did people make scientific notation?
(1 vote)
• In order to simplify numbers that are to big
• i am still confused how to solve questions of this type -
9 ten thousandths ; 10 hundred thousandths
• Hi there. you may be familiar with ten thousand or one hundred thousand. however, what you are talking about is decimal places. For example, 1000 would be one thousand. if you were to have a decimal which is basically a more specific version of a fraction. ".1" would be one-tenth, .01 would be one-hundredths, .001 would be one-thousandths, and so on. so if I had 1.5 it would be one and 5 tenths or 1 and a half.
• I have trouble using Scientific notation to the problems that I have at school for work.Any advice will be helpful.