You then add the resulting coefficients while keeping the power of 10 the same. To do that you move the decimal point of one coefficient to the left or right the number of places needed to make that number's power of 10 equal to the other. There is a second method for solving the above addition problem (not included in the calculated results), which requires converting the numbers to the same power of 10. Addition Steps (6 x 10 4) + (7 x 10 3) Factor out 1 of the powers of 10 = (6 x 10 4/10 4 + 7 x 10 3/10 4) x 10 4 Perform division of exponents: = (6 x 10 0 + 7 x 10 -1) x 10 4 Convert SN's to real numbers: = (6 + 0.7) x 10 4 Combine real numbers: = (6.7) x (10 4) Convert to proper SN: = 6.7 x 10 4 Here are the steps I use to solve the above addition problem. To add two SN's you factor out one of the powers of 10, convert the remaining scientific notations to real numbers, add the real numbers, and then convert that result to proper scientific notation format (if not already).Įxample addition problem: (6 x 10 4) + (7 x 10 3) Of course, this alternative method can be cumbersome if the numbers you are working with are very large or very small, and may not be possible if the calculator you are using won't display the results in regular notation. The other way to multiply scientific notations is to convert the notations to real numbers, perform the multiplication, and then convert the number back to scientific notation, like the following: Alternative Multiplication Method (3 x 10 6) x (6 x 10 4) = (3 x 1000000) x (6 x 10000) = 3000000 x 60000 = 180000000000 = 1.8 x 10 11 Multiplication Steps (3 x 10 6) x (6 x 10 4) Group like terms: = (3 x 6) x (10 6 x 10 4) Multiply coefficients and add exponents: = (18) x (10 10) Convert to proper SN: = 1.8 x 10 11 Here are the steps to solving the above problem. ('F-E' stands for 'fixed to exponent') The display is now showing the result in the 'shorthand' form which you can interpret as 6×10 7.To multiply two SN's you basically just multiply the coefficients and add the exponents, and then convert that result to proper scientific notation format (if not already).Įxample multiplication problem: (3 x 10 6) x (6 x 10 4) ![]() Do this by clicking the F-E button which you will find in the left half of the calculator keyboard. This is shown in its full form.įinally, you can force the calculator to display the result of the calculation in scientific notation. ![]() This tells the calculator that you want it to display the result of the calculation. You have now finished entering the term in the second set of brackets.Ĭlick the equal (=) button. The display is now showing the equivalent of 2×10 3. ![]() You will now start to enter the term in the second set of brackets. ![]() The display now changes to show the number you have entered in its full form (3×10 4= 30000). This tells the calculator that you want to multiply the number showing in the display by some other number. The display is now showing the equivalent of 3×10 4.You have now finished entering the term in the first set of brackets.Ĭlick the multiply (*) button. The 'e' now showing on the display indicates that the number you have entered is displayed in scientific notation.Įnter 4. ('Exp' stands for 'exponent'.) This tells the calculator that the next number you enter will be a power of 10 and that you are working in scientific notation. Make sure the Windows calculator is in Scientific mode by selecting Scientific from the View menu.Ĭlick the Exp button which you will find in the left half of the calculator keyboard.
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