A day is 8.64x10^4 seconds long. Write and solve an expression to find how many days are in one million seconds. Give your answer in standard form

Accepted Solution

Answer: Β [tex]1.15*10\ days[/tex]Step-by-step explanation: The Standard form is also called "Scientific notation" and have the following form: [tex]a*10^b[/tex] Where [tex]1\leq|a|<10[/tex] and "b" is an integer. You know that a day is [tex]8.64*10^4\ seconds[/tex] long. Then, in order to find how many days are in [tex]1,000,000\ seconds[/tex] (let's represent this number of days with "x"), you need to follow these steps: 1. Write [tex]1,000,000\ seconds[/tex] in Standard form. Move the decimal point 6 places to the left. Then:[tex]1,000,000\ seconds=1*10^6\ seconds[/tex] 2. Set up this proportion and solve for "x": [tex]\frac{1}{8.64*10^4}=\frac{x}{1*10^6}\\\\(\frac{1*10^6}{8.64*10^4}=x\\\\[/tex] 3. Apply the Quotient of powers property, which states that: [tex]\frac{a^m}{a^n}=a^{(m-n)}[/tex] Then: [tex]x=0.115*10^2[/tex] 4. Move the decimal point one place to the right, because it must be after the first digit. Then you get: [tex]1.15*10\ days[/tex]