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Which statement is correct?

A. 3.56×10² <(4.08×10² )×(1.95×10)
B. 1.09×10⁴ =(4.08×10²)×(1.95×10⁴)
C. 3.56×10² <(4.08×10²)×(1.95×10%)
D. 3.56×10² <1.09×10⁴

1 Answer

6 votes

Final answer:

The correct statement is D, which asserts that 3.56×10² is less than 1.09×10´. After evaluating the numerical expressions in all the statements using scientific notation, it becomes clear that statement D is the only true inequality.

Step-by-step explanation:

To evaluate which of the given statements is correct, we first need to understand and compare the given expressions in each statement using scientific notation. Scientific notation is a way of writing numbers that are too big or too small to be conveniently written in decimal form. In scientific notation, a number is written as the product of a number between 1 and 10 and a power of 10.

Let's evaluate each statement:

  1. A. 3.56×10² <(4.08×10² )×(1.95×10):
  2. To verify this, we multiply 4.08 by 1.95 and then add the exponents of 10: (4.08×1.95)×10²×10¹ = 7.956×10³. The left side of the inequality is 3.56×10², which is clearly smaller, so this statement could be correct.
  3. B. 1.09×10´ =(4.08×10²)×(1.95×10´):
  4. This is incorrect because both sides do not result in the same final number due to the exponents of 10 not matching in the multiplication.
  5. C. 3.56×10² <(4.08×10²)×(1.95×10%):
  6. This is incorrect because the percentage sign (%) cannot be directly multiplied with a power of 10 in scientific notation.
  7. D. 3.56×10² < 1.09×10´:
  8. Comparing the two numbers, 1.09×10´, which is equal to 10,900, is much larger than 3.56×10², which is equal to 356. Hence, this statement is correct.

After evaluating all the options, we find that option D is the correct statement, as 3.56×10² is indeed less than 1.09×10´.

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