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?

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

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

Yes, you are correct. Marcus's conclusion that the larger cell is 40 times greater in size than the smaller cell is accurate. However, his method of solving the equation is incorrect. To determine how many times greater the larger cell is, you would divide the size of the larger cell by the size of the smaller cell. In this case, it would be (2.0 * 10^-3) / (8.0 * 10^-4) = 2.5. Therefore, the larger cell is 2.5 times greater in size than the smaller cell, not 40 times.

Yes, you are correct. Marcus' answer of 40 is correct, but his reasoning and process to arrive at that answer is incorrect. Let's go through the correct process together:

To determine how many times greater the size of the larger cell is, we need to calculate the ratio of the sizes of the two cells. In this case, we are given that one cell measures 8.0 * 10^-4 centimeter across and the other cell measures 2.0 * 10^-3 centimeter across.

To compare the two cells, we can divide the size of the larger cell by the size of the smaller cell:

(2.0 * 10^-3 centimeter) / (8.0 * 10^-4 centimeter)

To divide these numbers, we need to rewrite them using the same exponent (magnitude):

2.0 * 10^-3 centimeter = (2.0 * 10^-3 centimeter) * (10^1 / 10^1) = 2.0 * (10^-3 * 10^1) centimeter = 2.0 * 10^-2 centimeter

8.0 * 10^-4 centimeter = (8.0 * 10^-4 centimeter) * (10^1 / 10^1) = 8.0 * (10^-4 * 10^1) centimeter = 8.0 * 10^-3 centimeter

Now we can substitute these values back into our ratio:

(2.0 * 10^-2 centimeter) / (8.0 * 10^-3 centimeter)

To simplify this fraction, we can divide the numerator by the denominator:

(2.0/8.0) * (10^-2/10^-3) = 0.25 * 10^-2/10^-3

To divide the powers of 10, we subtract the exponents:

0.25 * 10^-2/10^-3 = 0.25 * 10^(-2 - (-3)) = 0.25 * 10^-2 + 3 = 0.25 * 10^1 = 2.5

Therefore, the ratio of the sizes of the two cells is 2.5, meaning that the larger cell is 2.5 times greater in size than the smaller cell. Hence, Marcus' answer of 40 is incorrect, and the correct ratio is 2.5.