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Let's break down the numbers given in the problem and convert them to comparable formats so that we can arrange them in ascending order.

The numbers are:
1. \( 2.3 \times 10^{-2} \)
2. \( 93\% \)
3. \( -\sqrt{56} \)
4. \( -8 \frac{3}{4} \)

### Step 1: Convert all numbers into decimal form.

1. \( 2.3 \times 10^{-2} = 0.023 \)
2. \( 93\% = 0.93 \)
3. \( \sqrt{56} \approx 7.483 \) (but the given number is negative, so it’s \( -7.483 \))
4. \( -8 \frac{3}{4} = -8.75 \)

### Step 2: Now, let's order them from least to greatest.

- \( -8.75 \) (This is the smallest since it's most negative.)
- \( -7.483 \) (The next smallest, also negative.)
- \( 0.023 \) (A small positive number.)
- \( 0.93 \) (The largest positive number.)

### Final Order:
1. \( -8 \frac{3}{4} \)
2. \( -\sqrt{56} \)
3. \( 2.3 \times 10^{-2} \)
4. \( 93\% \)

Would you like a detailed explanation of any step? Here are five related questions to deepen understanding:

1. How do you convert percentages to decimals?
2. Why is the square root of a number considered irrational?
3. What is scientific notation, and how do you interpret it?
4. Can you explain how fractions are converted to decimals?
5. How do you compare negative numbers?

Tip: Always convert all the numbers to the same format (like decimals) before comparing them to avoid confusion.

Place the following in ascending order: 2.3 × 10^−2, 93%, −√56, −8 3/4.

Learn how to arrange numbers in ascending order using scientific notation, percentages, square roots, and fractions. This example includes converting a number in scientific notation, percentages to decimals, and calculating square roots.

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