Density Word Problem

Question

I saw this problem on Khan Academy and am still having trouble with this concept, but more importantly do not under the computation of a certain aspect of the problem:

Tanker= 2.5x10^3 m^3

Density of Steel= 8x10^3/m^3

Density of Seawater= 1X10^3/m3

In kilograms what total weight of seawater needs to be displaced in order to lift the tanker to the surface?

2.5x10^3 m^3 x 8x10^3kg=

2x10^7kg

My confusion at this point is the answer 2x10^7kg

I would think the answer was: 20x10^3

What am I not seeing?

Thanks

Answer 1

2.5x10^3 m^3 x 8x10^3kg

I see (2.5*8)= 20 and (10^3*10^3)=10^(3+3)=10^6

Next I see 20 x 10^6

Finally it looks like they interpret this as (2 *10^1) *10^6 and finally 2 *10^(1+6)= 2 *10^7.

Keep in mind that the problem starts with a 10^3 *10^3 the exponents add.

If you try it as 2500 * 8000 =20,000000 then put it in Scientific Notation you can count and see the 7 zeros.

You get 2 zeros from 2500 + 3 zeros from 8000 then two more zeros from 25 * 8 which is 200. I hope this helps. It is long and slow but it helps you to count, see and compare the number of zeros relative to the rules for multiplying exponents.

Answer 2

You are correct Sir!