Question

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

Answer 1

Answer:
`1.15*10\ days`

Explanation:

The Standard form is also called "Scientific notation" and have the following form:

`a*10^b`

Where
`1\leq|a|<10` and "b" is an integer.

You know that a day is
`8.64*10^4\ seconds` long.

Then, in order to find how many days are in
`1,000,000\ seconds` (let's represent this number of days with "x"), you need to follow these steps:

1. Write
`1,000,000\ seconds` in Standard form. Move the decimal point 6 places to the left. Then:

`1,000,000\ seconds=1*10^6\ seconds`

2. Set up this proportion and solve for "x":

`(1)/(8.64*10^4)=(x)/(1*10^6)\\\\((1*10^6)/(8.64*10^4)=x\\\\`

3. Apply the Quotient of powers property, which states that:

`(a^m)/(a^n)=a^((m-n))`

Then:

`x=0.115*10^2`

4. Move the decimal point one place to the right, because it must be after the first digit. Then you get:

`1.15*10\ days`