Question

Select the set of numbers that are arranged from least to greatest.

Answer 1

C

Explanation:

Answer 2

Scientific Notation

Any number in scientific notation is written in the following form:

`m*10^n`

Where m is a decimal number between 1 and 10 called the significand and n is an integer known as the exponent. If we have two different numbers written in scientific notation the one with the greatest exponent is the greater number. If they have the same exponent then the one with the greatest significand is the greater number.

Ordering the set

We have the following set of numbers in scientific notation:

`\begin{gathered} 1.6*10^(-5) \\ 1.62*10^(-4) \\ 1.7*10^(-5) \end{gathered}`

As I stated before, the one with the greatest exponent is the greatest number. We have two numbers with an exponent of -5 and one with an exponent of -4. Since -4 > -5 then the number with -4 as its exponent is the greatest.

Now let's study the other two numbers. They have the same exponent so the one with the greatest significand is the greatest. The significants are 1.6 and 1.7 so we get:

`1.7*10^(-5)>1.6*10^(-5)`

Now we can order the three numbers from least to greatest:

`1.6*10^(-5);1.7*10^(-5);1.62*10^(-4)`

Then the answer is option C.