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Dividing Scientific Notation | MathHelp.com
By MathHelp.com
To multiply numbers that are in written in scientific notation, such as 1.4 x 10 to the -2nd times 5.3 times 10 to the 6th, we first multiply the decimals, in this case 1.4 times 5.3, to get 7.42. Next, we multiply the powers of 10, in this case 10 to the -2nd times 10 to the 6th. Notice that we’re multiplying two powers that have like bases, so we add the exponents and leave the base the same, to get 10 to the -2 + 6, or 10 to the 4th. So we have 7.42 times 10 to the 4th. Finally, we’re asked to write our answer in scientific notation. Notice, however, that 7.42 times 10 to the -4th is already written in scientific notation, because we have a decimal between 1 and 10 that is multiplied by a power of 10. So we have our answer.
Multiplying Scientific Notation | MathHelp.com
By MathHelp.com
In this example, which involves natural logarithms, we’re asked to solve each of the following equations for x, and leave our answers in terms of e. To solve for x in the first equation, ln x = 3, we simply switch the equation from logarithmic to exponential form. Remember that ln x means the natural logarithm of x, and a natural log has a base of e. So, to convert the given equation to exponential form, remember that the base of the log represents the base of the power, the right side of the equation represents the exponent, and the number inside the log represents the result, so we have e…to the 3rd…= x, and we’ve solved for x. Notice that our answer, e cubed, is written in terms of e, which is what the problem asks us to do. Now, let’s take a look at the second equation, ln x squared = 8. Again, we solve for x by switching the equation from logarithmic to exponential form. Ln x squared means the natural logarithm of x squared, and a natural log has a base of e. So, converting the equation to exponential form, we have e…to the 8th…= x squared. Next, since x is squared, we take the square root of both sides. On the right, the square root of x squared is x. On the left, however, there are a couple of things to watch out for. First, remember that the square root of e to the 8th is the same thing as e to the 8th to the ½, which simplifies to e to the 8 times ½, or e to the 4th. Also, remember that when we take the square root of both sides of an equation, we use plus or minus, so our final answer is plus or minus e to the 4th = x.
Multiplying and Dividing by Powers of 10
By jimbabweiberg
The instructor uses an interactive white board to show that multiplying a decimal by 10 100 1 000 or 10 000 moves the decimal one two three or four places to the right. He displays a calculator to show this as well. He also explains and shows that dividing by a power of 10 moves the decimal place to the left according to the number of zeros in the number you are multiplying by.
[5.NBT.2-2.0] Multiplying/Dividing by 10 - Common Core Standard
By Front Row
Discover more Common Core Math at https://www.frontrowed.com Explain patterns in the placement of the decimal point when a decimal is multiplied by a power of 10, use whole-number exponents to denote powers of 10 Front Row is a free, adaptive, Common Core aligned math program for teachers and students in kindergarten through eighth grade. Front Row allows students to practice math at their own pace - learning advanced concepts when they're ready and receiving remediation when they struggle. Front Row provides teachers with access to a detailed data dashboard and weekly email reports that show which standards are causing students difficulty, what small groups can be formed for interventions, and how their students are progressing in math.Discover more Common Core Math at https://www.frontrowed.com
05 - Simplify Irrational Exponents, Part 1 (Radical Exponents, Powers, Pi & More)
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
01 - Simplify Rational Exponents (Fractional Exponents, Powers & Radicals) - Part 1
By Math and Science
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15 - What is a Logarithm (Log x) Function? (Calculate Logs, Applications, Log Bases)
By Math and Science
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ALL OF GRADE 9 MATH IN 60 MINUTES!!! (exam review part 1)
By Lumos Learning
Here is a great exam review video reviewing all of the main concepts you would have learned in the MPM1D grade 9 academic math course. The video is divided in to 3 parts. This is part 1: Algebra. The main topics in this section are exponent laws, polynomials, distributive property, and solving first degree equations. Please watch part 2 and 3 for a review of linear relations and geometry. If you watch all 3 parts, you will have reviewed all of grade 9 math in 60 minutes. Enjoy! Visit jensenmath.ca for more videos and course materials.
Learn Metric Units & Unit Conversions (Meters, Liters, Grams, & more) - [5-8-1]
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!
Converting Units With Conversion Factors - Metric System Review & Dimensional Analysis
By The Organic Chemistry Tutor
26 - Compound Interest Formula & Exponential Growth of Money - Part 1 - Calculate Compound Interest
By Math and Science
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Grade 5 Math - Multiplaction and Division of Powers of Ten 4
By Lumos Learning
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12 - What is Exponential Growth & Decay? (Half Life & Doubling Time) - Part 1
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!