To arrange the numbers $-1.7$, $-1 \frac{3}{4}$, and $-1 \frac{7}{9}$ from least to greatest, we'll first convert them to their decimal equivalents.

1. Decimal form of each number:

   • $-1.7$ is already in decimal form.
   • $-1 \frac{3}{4}$ can be converted by dividing 3 by 4: $-1 \frac{3}{4} = -1 - 0.75 = -1.75$
   • $-1 \frac{7}{9}$ can be converted by dividing 7 by 9: $-1 \frac{7}{9} = -1 - \left(\frac{7}{9}\right) \approx -1.7777...$

2. Arrange the numbers from least to greatest:

   The numbers in decimal form are:

   • $-1.7$
   • $-1.75$
   • $-1.7777...$

   Since we are working with negative numbers, the more negative a number is, the smaller it is. Thus, the order from least to greatest is:

   $-1 \frac{7}{9} \; (\approx -1.7777...), \; -1 \frac{3}{4} \; (-1.75), \; -1.7$

So, from least to greatest:
$-1 \frac{7}{9}, \; -1 \frac{3}{4}, \; -1.7$

Would you like more details, or do you have any other questions?

5 Related Questions:

1. How do you convert fractions to decimals?
2. How do you compare negative decimal numbers?
3. What are some strategies for ordering fractions without converting to decimals?
4. How can you compare positive and negative fractions directly?
5. Why does the negative sign affect the ordering of numbers differently?

Tip:

When comparing negative numbers, remember that a number with a larger absolute value is actually smaller (more negative) on the number line!