Question

which of the following is a quantity that could be represented by the number 2 x 10^-3
A.
the diameter (in meters) of an atom
B.
the time it takes (in minutes) to blink
C.
the occupancy limit of a pizza restaurant
D.
the annual salary of a high school math teacher

Answer 1

Your best guess? Reason out each response.

Answer 2

i honestly have no clue.

Answer 3

Hogwash.

D, Give a rough estimate of how many people you can cram into a pizza place.

1? 10? 100? 1/10? 1000? 0.001? 1000000?

Go.

Answer 4

100

Answer 5

Tiny ones? Maybe 10. So 10-100 or so. Perfect.

Sorry, that was C

Now D. High School Math Teacher's salary?

$1, $100, 10£, $100000

Go!

Answer 6

i would say like 100

Answer 7

I believe it is quite difficult to buy groceries for an entire year on $100. Guess bigger!

Answer 8

$100000

Answer 9

Fair enough. Maybe in Alaska! Anyway, let's agree to $10,000-$100,000.

A. Diameter of an atom (in meters)

1, 10, 0.01, 100, 0.0001, 1000, 0.000000001

What?

Answer 10

0.000000001

Answer 11

Good call. Look up the word "Angstrom". That's a good measurement and that's 10E(-10) M

B. Last one. Minutes to blink.

Go ahead and blink and estimate the number of SECONDS it takes to do that.

Answer 12

15 seconds maybe 10

Answer 13

?? I hope not. That would make it very difficult to operate a motor vehicle. Just a regular blink - not one you control.

Answer 14

Not the time between blinks. The time of the actual blink, itself.

Answer 15

1 second probably less

Answer 16

Good. I'd guess around 1/4 second.

If it is 1/4 seconds (0.25 seconds), how many minutes is that?

Answer 17

6?

Answer 18

??

0.25 seconds = 0.25/60 minutes = 0.0042 minutes

Answer 19

im so confused.

Answer 20

You are confused because you are trying to solve the world all in one grand gesture. This is perhaps the most difficult way to proceed. Just one piece at a time. That is all we are doing.

Recap

A.
the diameter (in meters) of an atom
1E(-9) Meters
B.
the time it takes (in minutes) to blink
4E(-3) Minutes
C.
the occupancy limit of a pizza restaurant
4E2 People
D.
the annual salary of a high school math teacher
5E4 Dollars

We just translated all those words into numerical equivalents. that was a lot of work that will get us to the answer. Are we there yet, no. What have we done so far? Translated words into mathematical expressions. This is a desirable and necessary skill.

What did we do?

Answer 21

What we seek is something in the neighborhood of 2E(-3). Any of ours anywhere near that?

Answer 22

so whats the answer

Answer 23

The answer is, you must THINK. That is the answer. The early study of mathematics is not nearly so much about finding the answer as it is training your brain to think - perhaps in a way that is not natural to everyone.