Add (6.3 × 10^7) + (4.2 × 10^6) and write your answer in scientific notation.
Understand the Problem
The question is asking to add the two numbers in scientific notation: (6.3 × 10^7) and (4.2 × 10^6). This involves aligning the exponents and performing the addition to arrive at the correct result in scientific notation.
Answer
$$6.72 \times 10^7$$
Answer for screen readers
$$6.72 \times 10^7$$
Steps to Solve
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Adjust the Exponents Since the two numbers have different exponents, we need to make them the same. We can convert (4.2 \times 10^6) to have the same exponent as (6.3 \times 10^7): $$ 4.2 \times 10^6 = 0.42 \times 10^7 $$
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Add the Coefficients Now we can add the coefficients since they are now in the same exponent: $$ 6.3 + 0.42 = 6.72 $$
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Write the Result in Scientific Notation The combined result can be expressed back in standard scientific notation: $$ 6.72 \times 10^7 $$
$$6.72 \times 10^7$$
More Information
The final result (6.72 \times 10^7) is now in scientific notation, representing a number significantly larger than either of the original numbers. Adding numbers in scientific notation often involves aligning exponents first to simplify the addition process.
Tips
- Not aligning exponents: It's important to adjust one of the numbers so they have the same exponent before adding.
- Forgetting to convert to proper scientific notation: After adding the numbers, ensure the result is expressed in standard form.
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