Question 5

0.1 < 0.101 < 0.11 < 0.7

The inequality 0.1 < 0.101 < 0.11 < 0.7 is true, as it accurately represents the increasing order of these decimal values from least to greatest.

A) 0.7 < 0.1 < 0.11 < 0.101

This option is incorrect because it suggests that 0.7 is less than 0.1, which is not true. In fact, 0.7 is greater than both 0.1 and the subsequent values, making this inequality false.

B) 0.1 < 0.7 < 0.101 < 0.11

This choice is incorrect as well. While it correctly places 0.1 and 0.7 in the correct order, it incorrectly positions 0.101 and 0.11. In reality, 0.11 is greater than 0.101, violating the order suggested here.

C) 0.1 < 0.7 < 0.11 < 0.101

This option is also incorrect. It places 0.11 incorrectly after 0.7 and before 0.101, which does not reflect the true values. The correct order shows that 0.101 is less than 0.11.

D) 0.1 < 0.101 < 0.11 < 0.7

This option is correct as it properly arranges the numbers in increasing order. Each subsequent number is indeed greater than the last, adhering to the principles of numerical inequality.

Conclusion

The correct answer, D, accurately reflects the true order of the decimal values from least to greatest. Options A, B, and C fail to maintain the correct relationships between the numbers, demonstrating that understanding the relative values of decimals is crucial in determining the validity of inequalities.