Question

Please help!

What is the order of 4 × 10^-7, 7 × 10^-9, 1 × 10^4, 2 × 10^4 from least to greatest?

A. 1 × 10^4, 2 × 10^4, 4 × 10^-7, 7 × 10^-9

B. 4 × 10^-7, 7 × 10^-9, 1 × 10^4, 2 × 10^4

C. 7 × 10^-9, 4 × 10^-7, 1 × 10^4, 2 × 10^4

D. 7 × 10^-9, 4 × 10^-7, 2 × 10^4, 2 × 10^4

Answer 1

7 x 10^-9
4 x 10^-7
1 x 10^4
2 x 10^4
Letter C

Answer 2

So, the smaller the exponent the smaller the number. So one that is -9 is very small.
We first want to compare the numbers through the exponents.

-9 is the lowest exponent, meaning it is the smallest number, so any answer that doesn't start with 7×10^-9 is incorrect

Meaning we can cross out answer choices A and B

-7 is the next to smallest exponent, but Choices C and D both have 4×10^-7 as the second, so we cannot out anymore answers.

After that the final two numbers each have the same exponent, so then we look at the actual numbers.

Which are 1 and 2, they are each risen to the 4th power, meaning they have 4 zero's after the number.
So the two numbers we have are 10000 and 20000

10000 is less than 20000, so that means 1×10^4 comes next in our ordering of least to greatest, leaving 2×10^4 as the greatest

So we order them properly from least to greatest, and our chart is:

7×10^-9 < 4×10^-7 < 1×10^4 < 2×10^4

This is the same as answer choice C, so C is your answer! Hopefully this all makes sense!