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### Course: Algebra basics>Unit 6

Lesson 4: Scientific notation intro

# Multiplying in scientific notation example

Scientific notation shows a number (greater than or equal to 1 and less than 10) times a power of 10. To multiply two numbers in scientific notation, we can rearrange the equation with the associative and commutative properties. If the final product is not in scientific notation, we can regroup a factor of 10. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Why would you use scientific notation in real life
• Faster communication is why. Scientists publish their results in papers, give presentations, and frequently work in groups in labs. All of this requires formatting numbers to make it easy for others to see and use. Often these numbers are very, very large, or very, very small. It's difficult, annoying, and time-consuming to make comparisons where you have to count all the zeroes each and every time.

For example, which number is bigger: 5500000000000000000 or 55000000000000000000? Wouldn't it be faster and easier to answer this question with 5.5*10^18 versus 5.5x10^19?
• what if the there is two negative -5 what you do
• 10^-5 * 10^-5 would be 10^(-5 + -5) = 10^-10. When we multiply everything out, we would get 29.12 x 10^-10 which is correct numerically but not quite correct scientific notation. We could rewrite 29.12 as (2.912 x 10) so our answer would be (2.912 x 10) x 10^-10 = 2.912 * 10^-9
• The point of the video is to Multiply and Divide Scientific Notation, right? So how come at you add? Is it something about exponent rules? If so, can someone please explain it, and, if not, can someone please tell me how? Thanks. And also, why do you have to change the number at ? Thanks in advance for the help.
• Its an exponent rule. 10^2 x 10^3 is equal to 10^(2+3) because (10 x 10)x(10 x 10 x 10)= 10^5
• where are you going to need this in life or what job
• When you have to write a really huge number, like 159,000,000,000,000,000,000,000,000, scientific notation will come in handy. In physics, scientific notation is especially useful. Really really big numbers show up often, and they will most likely be written in scientific notation.
• As an engineer and mathematician, I have long added a step with my students as to how to finish off operations with scientific notation, and I would like some feedback on this, please. Scientific notation serves TWO functions: to show at a glance how big (or small) a number is; and... to show how accurately that number is known via the number of digits in the significand (or coefficient or mantissa, as it is sometimes called). When multiplying or dividing two numbers together in scientific notation, the answer should not be represented as MORE accurately known than either of the original numbers. Thus, I have always given my students a rough guideline for how to round the final answer to more appropriately display the proper accuracy. The guideline I use is to inspect the number of digits given in each significand, rounding the answer to the least number of digits in the two original numbers. As such, in the video above, I would have rounded the significand in the final answer to 2.9 (NOT 2.912), since each of the two original numbers only had two digits of accuracy in them. (9.1 and 3.2.) This is not perfect, but it is a simple method to roughly account for the fact that accuracy cannot improve just from multiplying two inaccurate numbers together! Any thoughts on my guideline and why something similar to it is not commonly used when teaching operations in scientific notation?
• When you are moving digits for the scientific notation, moving to left increasing and to the decreasing right?
• Moving the decimal point to the left increases the exponent and moving it to the right decreases the exponent of 10, if it's that that you mean.
• What are you suppose to do when it's .34 or something? He doesn't explain that, and those are in the questions you have to do after the video.
• we learned about this in my math class. you just do it negative, and the decimal goes after the first digit that isn't 0. for example, .34 would be 3.4e-1 !
• Define scientific notation specifically?
• Scientific notation is a mathematical expression used to represent a decimal number between 1 and 10 multiplied by ten, so you can write large numbers using less digits.
• why did it go to 2 when it 10 to the 1st
• He's writing the final answer in the form of scientific notation: 2.912 * 10^2.

29.12 x 10^1 is equal to 2.912 x 10^2, they'll give you the same number. But 29.12 x 10^1 is not in the correct form of scientific notation.
(1 vote)
• how would I solve the following:
(2.0^3)^2 x 10^2