Question

Which of the following has the largest value?

• A. $0.0001$
• B. $\frac{1}{10000}$
• C. $\frac{1}{{10}^6}$
• D. $\frac{1}{{10}^6}÷0.1$

Answer 1

Answer: (A), (B)

$\frac{1}{10000}$

Step 1. Explanation for the correct option.

Option B :$\frac{1}{10000}$

Use the properties of exponents to simplify the expression $\frac{1}{10000}$:

So, $\frac{1}{10000}=0.0001$

Option A and Option B are equal and have largest value.

Step 2. Explanation for the incorrect options.

Similarly, simplify the expressions $\frac{1}{{10}^6}$ and $\frac{1}{{10}^6}÷0.1$:

$\begin{array}{rcl}\frac{1}{{10}^6}& =& \frac{1}{1000000}\\ & \Rightarrow & \frac{1}{{10}^6}=0.000001\end{array}$

And

$$\begin{gathered} \frac{1}{{10}^6}÷0.1=\frac{1}{1000000}\times 10 \\ \Rightarrow \frac{1}{{10}^6}÷0.1=\frac{1}{100000} \\ \Rightarrow \frac{1}{{10}^6}÷0.1=0.00001 \end{gathered}$$

The smallest decimal value is $0.000001$ which is equal to $\frac{1}{{10}^6}$.

So, the correct options are (A) and (B).