ultiplying Scientific Notation to Solve a Real-World ProblemIn 1867, the United States purchased Alaska from Russia. Alaska is about 5.9 × 105 square miles. The United States paid about $12.20 per square mile. Approximately how much did the United States pay Russia for Alaska?Complete the steps to answer the question.1. Write the expression: (5.9 × 105)(12.2)2. Multiply the decimal values: × 1053. Write in scientific notation: × The United States paid Russia approximately for Alas

Accepted Solution

Answer:$ [tex]7.198*10^{6}[/tex]Step-by-step explanation:First of all, we know the approximate area of Alaska, which is [tex]5.9*10^{5}[/tex] square miles, or [tex]5.9*10^{5}[/tex] [tex]mi^{2}[/tex]. We also know how much The United States paid for each square mile: $[tex]12.20[/tex], or [tex]12.20[/tex] $[tex]/mi^{2}[/tex]. If we multiply these numbers, we get the approximate amount that The United States paid Russia for Alaska. That is:Step 1. We write the expression to calculate how much The United States paid Russia for Alaska:[tex](5.9*10^{5}[/tex] [tex]mi^{2})[/tex] [tex]*[/tex] [tex](12.20[/tex]$[tex]/mi^{2})[/tex] Step 2. We multiply the decimal values and calculate the amount the United States paid Russia:[tex](5.9*10^{5}[/tex] [tex]mi^{2})[/tex] [tex]*[/tex] [tex](12.20[/tex]$[tex]/mi^{2})[/tex] = [tex](590 000[/tex] [tex]mi^{2})[/tex] [tex]*[/tex] [tex](12.20[/tex]$[tex]/mi^{2})[/tex]= 7 198 000 $Note that the [tex]mi^{2}[/tex] units cancel each other out, because one [tex]mi^{2}[/tex] was multiplying (the one in the area of Alaska), while the other [tex]mi^{2}[/tex] was dividing (the one below $, which indicated dollars per square mile).Step 3. We write the result in scientific notation.  For this step, we should know that for scientific notation we only use one integer followed by decimals.  Since we have a big number (7 198 000), we must “shrink” it down by running a comma from right to left by a certain amount of places.  In order to get to only one integer, let’s see how many times we have to displace the comma from right to left:7 198 000719 800.0    (1)71 980.00    (2)7 198.000    (3)719.8000    (4)71.98000    (5)7.198000    (6)= 7.198Since we had to move the comma six places from right to left in order to “shrink” our big number, we now must express the scientific notation by using an exponent of 6:Answer: $ [tex]7.198*10^{6}[/tex]