Based on the 2nd rule of exponents,a student comes up with 1000 - 10 = 100. How do I show how that is wrong?

Answer 1

I guess the student assumed that 10^3 - 10^1 = 10^2?

"How do I show how that is wrong?"
Uh, because 1000 - 10 = 990, and not 100?

Answer 2

Just remind the student that the order of operations must be followed. Before you add or subtract numbers you must make sure that they don't have a higher order attached to them. Simply show them that the problem requires the exponents to be solved before the subtraction. Tell them to think of the problem in this fashion

10^3 - 10^1=x
10^3=10*10*10 therfor 10^3=1000
10^1=10
since we have determined that 10^3=1000 and 10^1=10
it is easier to understand that the original problem is"

1000-10=990

The easiest way to teach a student to avoid this is that The Mathematical Order of Operations takes precedent in any equation. For instance in this problem the would know that one must first solve exponants and then solve the subtraction. You will find this true in most of the problems students have with math. The order of operations must be obeyed...it is the law.

Answer 3

You don't subtract the exponents unless you divide the numbers.

1*10^4 - 1*10^1 is always 990

they can't use that trick unless they divide or multiply the numbers, that is simple enough.

1*10^4 / 1*10^1 is always 1*10^3

Perhaps going over what exponents are again (multiplying something by itself that many times... not multiplying it by that number, et cetera) would be helpful.

Answer 4

It's clear that they don't understand the laws of exponents *or* how scientific notation works.

I'd suggest an hour of extra training on the subject after school followed by an auxilliary set of exercises (about 100 of them) involving scientific notation.

Repeat as necessary.


Doug

Answer 5

When you add or subtract numbers with exponents, you don't add or subtract the exponent itself.

Answer 6

What does this question have to do with astronomy and space ???