Question 29

6.0 × 10¹⁰

To find an expression equivalent to 1200 X (5 X 10⁷), we first calculate the product. Multiplying 1200 by 5 gives us 6000, and when we shift this value using scientific notation, we can express it as 6.0 × 10³. Combining this with 10⁷, we add the exponents to get 6.0 × 10¹⁰.

A) 12X10¹⁰

This option is incorrect because while the base number is in the correct order of magnitude, the coefficient 12 does not accurately reflect the multiplication of 1200 and 5. The correct coefficient derived from the calculation is 6.0, not 12.

B) 6.0 × 10¹⁰

This option is correct as it accurately represents the product of 1200 and 5 multiplied by 10⁷. The calculations yield 6000, which is expressed as 6.0 × 10³ when combined with 10⁷ results in the correct expression of 6.0 × 10¹⁰.

C) 6.0X10¹¹

This option is incorrect because it implies an incorrect exponent. The calculated product should yield a total exponent of 10, not 11. Therefore, this does not accurately represent the original expression.

D) 7.2X10¹³

This option is also incorrect. The coefficient of 7.2 suggests a much larger product than what is obtained from the original expression. Upon multiplying 1200 by 5, the resulting product does not equate to anything in the order of magnitude suggested by this expression.

E) 9.4X10¹⁴

This option is incorrect as it suggests an even larger value than the other incorrect options. The coefficient of 9.4 and the exponent of 14 diverge significantly from the calculated product of 1200 X (5 X 10⁷).

Conclusion

The correct answer, 6.0 × 10¹⁰, accurately reflects the multiplication of 1200 by 5 and the subsequent adjustment of the scientific notation. All other options either miscalculate the coefficient or the exponents, thus failing to represent the original expression correctly. This demonstrates the importance of understanding how to manipulate scientific notation in calculations.