express the volume of a fish tank shown below in scientific notation when h=7000 mm, w=6000, and I=8000mm.

Question

it is a word problem that needs to be solved. The answer must go in this form ___x10____mm³

Answer 1

The form of the answer is in scientific notation which means we need a few rules of exponents to work with.

 

First... Scientific notation always lists values as being multiplied by 10 to some power (exponent). The power is determined by how many steps we have to take to move our decimal behind the first numerical value (1-9) in our number.

 

For example: The number 7,000 would require us to move the decimal 3 times to get it behind the 7. This 3 will then become our exponent.

 

7,000 = 7 x 10³   ...Follow the same steps for the other values...

6,000 = 6 x 10³

8,000 = 8 x 10³

 

Because the question is referring to Volume, we know that we have to multiply these three values (V=L x W x H)

When multiplying numbers in scientific notation, we have to remember the product rule of exponents which states:

X^a•X^b = X^a+b  (I'm using the dot to represent multiplication so that it's easier to see with the variables) 

 

 

This means that when we multiply values of the same base with exponents, we add the exponents.

So, the values in front of ( x 10³) we treat them as coefficients and multiply them separately. We use the power rule on the rest...

 

7 x 10³ • 6 x 10³ • 8 x 10³ 

 

= (7 x 6 x 8) • 10³ • 10³ • 10³

 

= 336 x 10³⁺³⁺³

 

= 336 x 10⁹

You can check your answer by multiplying 7000x6000x8000 to get 336,000,000,000. You'll have to move the decimal over 9 times to the left to get behind the 6 of 336.

 

I hope this helps!