Question 27

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

To find the expression equivalent to 1,200(5 * 10^7), we can multiply 1,200 by 5 and adjust the powers of ten accordingly, resulting in 6 * 10^10.

A) 1.2 * 10^10

This option is incorrect because while it presents a valid scientific notation, it does not reflect the correct multiplication of 1,200 and 5. The result of that multiplication should yield a larger coefficient.

B) 6 * 10^10

This option is correct as it accurately represents the product of 1,200 and 5. When calculated, 1,200 times 5 equals 6,000, which can be expressed as 6 * 10^3 when adjusted with the power of ten from 10^7, leading to 6 * 10^(3+7) = 6 * 10^10.

C) 6 * 10^31

This option is incorrect because it significantly overestimates the power of ten. The calculation of 1,200(5 * 10^7) does not produce a result that approaches 10^31; instead, it results in a much lower exponent.

D) 7.2 * 10^13

This option is incorrect as it also miscalculates the coefficient and the power of ten. The result from the multiplication does not align with this power, leading to an incorrect representation.

E) 9.4 * 10^34

This option is incorrect as it vastly overshoots both the coefficient and the exponent. The result of the multiplication is nowhere near the size represented by this option.

Conclusion

The correct answer, 6 * 10^10, is derived from the accurate multiplication of 1,200 and 5, followed by the correct adjustment of the exponent. All other options fail because they either miscalculate the coefficient or the exponent, leading to incorrect representations of the product.