To solve this problem, we need to compare and order the given rational numbers from least to greatest. The numbers provided are:

$-16 \dfrac{7}{28}, \quad 16 \dfrac{7}{25}, \quad -16, \quad \dfrac{12}{25}$

Let's break it down step by step:

1. Convert Mixed Fractions to Decimals

First, let's convert each number into a decimal form for easier comparison.

• $-16 \dfrac{7}{28}$ is a mixed number. The fraction $\dfrac{7}{28} = \dfrac{1}{4} = 0.25$, so: $-16 \dfrac{7}{28} = -16.25$

• $16 \dfrac{7}{25}$ is also a mixed number. The fraction $\dfrac{7}{25} = 0.28$, so: $16 \dfrac{7}{25} = 16.28$

• $-16$ is already an integer, so: $-16 = -16$

• $\dfrac{12}{25} = 0.48$

2. Compare the Values

Now, we have the following decimal values:

$-16.25, \quad 16.28, \quad -16, \quad 0.48$

Now, we can clearly order them from least to greatest:

$-16.25, \quad -16, \quad 0.48, \quad 16.28$

3. Conclusion

The numbers in order from least to greatest are:

$-16 \dfrac{7}{28}, \quad -16, \quad \dfrac{12}{25}, \quad 16 \dfrac{7}{25}$

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How do you convert a mixed fraction into a decimal?
2. What is the difference between proper fractions and mixed numbers?
3. Can a fraction ever be larger than its whole number part when comparing mixed numbers?
4. How can comparing fractions with different denominators be simplified?
5. What is the method for ordering positive and negative rational numbers?

Tip: When ordering negative numbers, remember that a number farther from zero is actually smaller.