Question

The diameter of a grain of sand measures at about 0.0046 inches, while the diameter of a dust particle measured at about 0.00005 inches. About how many times larger is the diameter of a grain of sand than a dust particle? Estimate the following problem using powers of 10.

Answer 1

To approximate how many times larger the diameter of a grain of sand is compared to a dust particle using powers of 10, the grain of sand at 5 x 10^-3 inches is about 100 times larger than a dust particle at 5 x 10^-5 inches.

Step-by-step explanation:

The student is asking how many times larger the diameter of a grain of sand is when compared to the diameter of a dust particle, using powers of 10 for estimation. To find the answer, we take the diameter of a grain of sand (0.0046 inches) and divide it by the diameter of a dust particle (0.00005 inches).

0.0046 inches / 0.00005 inches = 92 times larger.

When we estimate using powers of 10, we can round the diameter of a grain of sand to 0.005 (5 x 10-3 inches) and the diameter of a dust particle to 0.00005 (5 x 10-5 inches). Using powers of 10 for easier computation, we can see that the grain of sand is approximately 100 times larger than a dust particle, because 5 x 10-3 is two orders of magnitude or 102 times larger than 5 x 10-5.

Answer 2

We have the following:

To know how many times one grain is bigger than the other, we must calculate the quotient of them, as follows:

`(0.0046)/(0.00005)=(4.6\cdot10^(-3))/(5\cdot10^(-5))=0.92\cdot10^(-3-(-5))=0.92\cdot10^2=92`

Therefore it is 92 times larger