Calculate $(6 \times 10^8) (7 \times 10^{-7})$
Understand the Problem
The question requires calculating the product of two numbers expressed in scientific notation. We will multiply the coefficients and add the exponents of 10 to find the result in scientific notation.
Answer
$4.2 \times 10^2$
Answer for screen readers
$4.2 \times 10^2$
Steps to Solve
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Multiply the coefficients Multiply the coefficients of the numbers in scientific notation: $6 \times 7 = 42$
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Add the exponents Add the exponents of the powers of 10: $10^8 \times 10^{-7} = 10^{(8 + (-7))} = 10^1$
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Combine the results Combine the result of the coefficients and the exponents: $42 \times 10^1$
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Convert to scientific notation To write the number in proper scientific notation, we need the coefficient to be between 1 and 10. Therefore, we rewrite $42$ as $4.2 \times 10^1$. Then we have: $42 \times 10^1 = (4.2 \times 10^1) \times 10^1 = 4.2 \times 10^{(1+1)} = 4.2 \times 10^2$
$4.2 \times 10^2$
More Information
Scientific notation is a way of expressing numbers that are too big or too small to be conveniently written in decimal form. It is commonly used in science and engineering.
Tips
A common mistake is to forget to adjust the exponent after making the coefficient a number between 1 and 10. For example, students might get $42 \times 10^1$ and stop there, not converting to proper scientific notation. Another mistake is to multiply the exponents instead of adding them.
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