3×10−141031033×10 −14 ​  Give your final answer in scientific notation rounded to two decimal places.

1. Break Down the Problem

We need to simplify the expression $3 \times 10^{-14} - 10^{31} \times 10^{-14}$.

2. Relevant Concepts

We can use the properties of exponents to simplify the expression. Recall that: $a^m \times a^n = a^{m+n}$ Also, subtracting numbers in scientific notation requires the non-scientific part (the coefficients) to be expressed using the same power of ten.

3. Analysis and Detail

1. Simplify $10^{31} \times 10^{-14}$: $10^{31} \times 10^{-14} = 10^{31 - 14} = 10^{17}$ Consequently, $10^{31} \times 10^{-14} = 10^{17}.$

2. Now rewrite the original expression: $3 \times 10^{-14} - 10^{17}.$

3. To subtract these two terms, we need to express $10^{17}$ in terms of $10^{-14}$: $10^{17} = 10^{17} \times \frac{10^{-14}}{10^{-14}} = 10^{3} \times 10^{-14} = 1000 \times 10^{-14}.$

4. Now we substitute this back into the expression: $3 \times 10^{-14} - 1000 \times 10^{-14} = (3 - 1000) \times 10^{-14} = -997 \times 10^{-14}.$

4. Verify and Summarize

The final simplified form is: $-997 \times 10^{-14}.$ To convert this into proper scientific notation, we express $-997$ as $-9.97 \times 10^2$: $-997 \times 10^{-14} = -9.97 \times 10^{2} \times 10^{-14} = -9.97 \times 10^{-12}.$

Final Answer

The final result in scientific notation rounded to two decimal places is: $\boxed{-9.97 \times 10^{-12}}.$