Evaluate $\frac{0.00000231}{0.007}$ and leave the answer in standard form

To solve this problem, we need to express the numbers in standard form (scientific notation) to make the division easier to handle.

1. Analyze the question

We are asked to evaluate the expression:

And ensure the final result is in standard form ($a \times 10^n$, where $1 \leq a < 10$).

2. Explain the concept

Standard form allows us to write very small or very large numbers as a product of a number between 1 and 10 and a power of 10.

• For $0.00000231$: Move the decimal point 6 places to the right to get $2.31$. Since we moved to the right, the exponent is negative: $2.31 \times 10^{-6}$.
• For $0.007$: Move the decimal point 3 places to the right to get $7$. The exponent is negative: $7 \times 10^{-3}$.

3. Show the solution

Now, substitute these into the expression:

Step 1: Divide the coefficients

Step 2: Divide the powers of 10 Using the law of indices ($\frac{a^m}{a^n} = a^{m-n}$):

Step 3: Combine the results

Step 4: Convert to proper standard form The coefficient $0.33$ is not between 1 and 10. We must move the decimal one place to the right to get $3.3$. Moving the decimal to the right decreases the exponent by 1:

4. Identify the answer

Comparing our result to the given options, we find it matches option A.

5. Exam Tip

When dividing decimals, it is often easier to multiply both the numerator and denominator by a power of 10 (like $10^6$ or $10^7$) to remove the decimals entirely before dividing. Also, always double-check your sign when subtracting negative exponents—many students mistakenly calculate $-6 - 3$ instead of $-6 - (-3)$.