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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 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.
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.
Units of Measurement | MathHelp.com
By MathHelp.com
This lesson covers vertical angles. Students learn the definition of vertical angles and the vertical angle theorem, and are asked to find the measures of vertical angles using Algebra. Students also solve two-column proofs involving vertical angles.
Multiplying and dividing with significant figures | Decimals | Pre-Algebra | Khan Academy
By Khan Academy
This video takes us through some real world examples of when we should use significant figures when multiplying and dividing. An important note: never consider significant figures until you have reached your FINAL ANSWER. Otherwise, rounding too early will produce more uncertainty about your solution.
Learn to Convert Decimals to Fractions (Change a Decimal into a Fraction) - [21]
By Math and Science
Quality Math And Science Videos that feature step-by-step example problems!