Add (6.2 × 10²) + (3.934 × 10³) and write your answer in scientific notation.
Understand the Problem
The question is asking to add two numbers in scientific notation, specifically (6.2 × 10²) and (3.934 × 10³), and then provide the answer in scientific notation.
Answer
The answer is $4.00 \times 10^3$.
Answer for screen readers
The final answer is $4.00 \times 10^3$.
Steps to Solve
- Align the Exponents
Before we can add the numbers, we need to have them in the same scientific notation format. The first number is $6.2 \times 10^2$, and the second number is $3.934 \times 10^3$. We can convert $6.2 \times 10^2$ to a form with a base of $10^3$ by adjusting the decimal point:
$$ 6.2 \times 10^2 = 0.062 \times 10^3 $$
- Add the Coefficients
Now that both numbers are expressed in terms of $10^3$, we can add the coefficients:
$$ 0.062 + 3.934 = 3.996 $$
- Combine Coefficients with the Common Base
We now write the result in scientific notation:
$$ 3.996 \times 10^3 $$
- Adjust for Significant Figures (if necessary)
Check if the answer is consistent with significant figures. Since both original numbers have three significant figures, we round $3.996$ to three significant figures:
$$ 4.00 \times 10^3 $$
The final answer is $4.00 \times 10^3$.
More Information
In scientific notation, the number must be expressed as a coefficient between 1 and 10 multiplied by a power of 10. Here, the sum $4.00 \times 10^3$ maintains proper format and significant figures.
Tips
- Forgetting to align the exponents before adding the coefficients.
- Not converting the coefficients to the same power of ten, which can lead to incorrect sums.
- Rounding too early or not considering significant figures correctly.
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