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Which statement is correct?

A. 3.56 x 10²/109 x 10⁴ ≤ (4.08 x 10²(1.95x10⁻⁶)
B. 3.56 x 10²/109 x 10⁴ < (4.08 x 10²(1.95x10⁻⁶)
C. 3.56 x 10²/109 x 10⁴ > (4.08 x 10²(1.95x10⁻⁶)
D. 3.56 x 10²/109 x 10⁴ = (4.08 x 10²(1.95x10⁻⁶)

1 Answer

3 votes

Final answer:

After evaluating both expressions and expressing them in proper scientific notation, the LHS is 3.266 x 10^-4 and the RHS is 7.956 x 10^-4. Therefore, the LHS is less than the RHS, and the correct statement is option B. Thus, the correct statement is B. 3.56 x 10²/109 x 10´ < (4.08 x 10²)(1.95x10⁻¶)

Step-by-step explanation:

To determine which statement is correct, we need to compare the values of the expressions given in the statements. Let's first evaluate each side of the inequalities given in the options A to D.

For the left-hand side (LHS) expression, we have:
3.56 x 10² / 109 x 10⁴
This simplifies to:
(3.56 / 109) x (10² / 10⁴)
0.03266 x 10⁻²
We can now put this value in proper scientific notation:

3.266 x 10⁻´
For the right-hand side (RHS) expression, we have:

4.08 x 10² x 1.95 x 10⁻¶

When multiplying, we add the exponents:

4.08 x 1.95 x 10² x 10⁻¶
Now, evaluate the multiplication:
7.956 x 10⁻⁴
Now that we have both the LHS and RHS evaluated and expressed in proper scientific notation, we can compare them:

LHS = 3.266 x 10⁻´
RHS = 7.956 x 10⁻⁴
Since 3.266 is less than 7.956 and both expressions have the same power of ten, we can clearly see that:

3.266 x 10⁻´ < 7.956 x 10⁻⁴
Thus, the correct statement is B. 3.56 x 10²/109 x 10´ < (4.08 x 10²)(1.95x10⁻¶)

User Sachin Midha
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