Add (6.2 × 10²) + (3.934 × 10³). Write your answer in scientific notation.
Understand the Problem
The question is asking to add two numbers expressed in scientific notation, specifically (6.2 × 10²) and (3.934 × 10³). The result should also be written in scientific notation.
Answer
$4.554 \times 10^3$
Answer for screen readers
The final answer is $4.554 \times 10^3$.
Steps to Solve
- Write the numbers in a common format Both numbers need to be expressed with the same exponent. We will convert $6.2 \times 10^2$ to be in terms of $10^3$.
To do this, we multiply $6.2 \times 10^2$ by $10^{1}$:
$$ 6.2 \times 10^2 = 6.2 \times 10^2 \cdot \frac{10}{10} = 6.2 \times 1.0 \times 10^3 = 0.62 \times 10^3 $$
- Add the two numbers Now we can add $0.62 \times 10^3$ and $3.934 \times 10^3$:
$$ (0.62 + 3.934) \times 10^3 $$
Calculating the addition gives:
$$ 4.554 \times 10^3 $$
- Result in scientific notation The result must be expressed in scientific notation.
The addition has been done already, and the result is in correct scientific notation:
$$ 4.554 \times 10^3 $$
The final answer is $4.554 \times 10^3$.
More Information
The sum of the numbers in scientific notation was calculated by first converting them to a common exponent, enabling straightforward addition. The final result remains in scientific notation, which is a standard format for expressing large numbers.
Tips
- Forgetting to match the exponents before adding can lead to incorrect results. Always ensure that both terms have the same exponent when adding or subtracting in scientific notation.
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