Algebra Test 3 #13

Question: Test 3, Number 13: Answer book says number gets smaller by 7. Yes, the number gets 7 digits smaller but the question is asking about what happens to the exponent – doesn’t the exponent get larger by 7? That’s what we were thinking but we are no experts so here we are asking! Thanks!

Answer: When you are moving to the left with the decimal, the exponent is getting smaller. Let’s work through an example to show you what I mean:

If we start with the number 6,000

That’s 6 x 10^3 in scientific notation.

If I take the decimal in 6,000 and move it 7 places to the left I end up with

.0006000 = .0006 = 6 x 10^ -4

Notice that the exponent goes from 3, to –4, which is a difference of 7 digits in the negative direction. So we say the exponent gets 7 digits smaller.

I hope this helps!