Question

Marcus studies two plant cells in biology class. One cell measures 8.0 * 10^-4 centimeter across. The other cell measures 2.0 * 10^-3 centimeter across. Marcus wants to know how many times greater the size of the larger cell is. He concludes that the larger cell is 40 times greater in size than the smaller cell.

He solved the equation like: 8/2=4. 10^-3/10^-4=10^1=10. 4*10=40.

Is his answer and process correct?



I think he is correct with it being 40,but I don't think that the way he did it was right. Am I right?

Answer 1

incorrect,
first of all
2.0 * 10^-3 > 8.0 * 10^-4
so he should have divided 2.0 * 10^-3/(8.0 * 10^-4)
= 2/8 * 10^-3/10^-4
= .25 x 10^1
= 2.5

So the larger is 2.5 times as large as the smaller

check: 8.0 * 10^-4 = 0.0008
2.0 * 10^-3 = 0.002 , notice .002 > .0008
and .002/.0008 = 20/8 = 2.5

Answer 2

he's wrong, since 10^-3 is greater than 10^-4.
If you just consider the diameters of the cells, the ratio is
(2.0 * 10^-3) / (8.0 * 10^-4) = (2.0/8.0) * (10^-3 / 10^-4) = 0.25 * 10^1 = 2.5
The larger cell is 2.5 times as big across as the smaller cell.

However, its area is 2.5^2 = 6.25 times as large.

The division shown as his method is just screwy, since he is trying to divide

(a*b)/(c*d) but splits it up into
a/c * d/b