Which of the following expressions is equivalent to 1,200(5 * 10^7)?

Rationale

1,200(5 * 10^7) is equivalent to 6 * 10^10.

To simplify the expression, first calculate 1,200 multiplied by 5, which equals 6,000. Then, express 6,000 in scientific notation as 6 * 10^3. Finally, multiply this by 10^7, leading to 6 * 10^(3+7) or 6 * 10^10.

A (1.2 * 10^10) YOUR ANSWER

This option suggests a different coefficient of 1.2 and an exponent of 10, which does not match our calculations. The correct coefficient derived from the multiplication process is 6, not 1.2, indicating that this expression is not equivalent.

B (6 * 10^10) CORRECT

This choice accurately reflects the result of simplifying the original expression. By calculating 1,200 times 5, we arrive at 6,000, which is correctly expressed as 6 * 10^10 in scientific notation, confirming this as the correct answer.

C (6 * 10^31) YOUR ANSWER

This option incorrectly increases the exponent significantly. While the coefficient is correct, the exponent does not reflect the correct sum derived from adding 3 and 7, which is 10, not 31. Thus, this expression cannot be equivalent to the original.

D (7.2 * 10^13) YOUR ANSWER

This expression presents a coefficient of 7.2 and an exponent of 13, which are inconsistent with our calculations. The multiplication results in a coefficient of 6 and an exponent of 10, making this option incorrect.

E (9.4 * 10^34) YOUR ANSWER

This choice introduces both an incorrect coefficient and an unrealistic exponent. The calculation does not support these values, as the origin of the multiplication leads us to a much smaller exponent and coefficient than presented here.

Conclusion

The simplification of the expression 1,200(5 * 10^7) confirms that it is equivalent to 6 * 10^10. Each incorrect choice fails to match the required coefficient or exponent derived from the multiplication process, reinforcing the accuracy of the correct answer. Understanding scientific notation is crucial for ensuring the correct representation of numerical values.