Determine the value of each expression. Then, place the expressions in order from least value to greatest value.

Question

37.8/10^1 37.8x10^2 37.8/10^3 37.8/10^2 37.8x10^1

Answer 1

Let's evaluate each expression:

1. \( 37.8 / 10^1 \): \[ 37.8 / 10^1 = 37.8 / 10 = 3.78 \]

2. \( 37.8 \times 10^2 \): \[ 37.8 \times 10^2 = 37.8 \times 100 = 3780 \]

3. \( 37.8 / 10^3 \): \[ 37.8 / 10^3 = 37.8 / 1000 = 0.0378 \]

4. \( 37.8 / 10^2 \): \[ 37.8 / 10^2 = 37.8 / 100 = 0.378 \]

5. \( 37.8 \times 10^1 \): \[ 37.8 \times 10^1 = 37.8 \times 10 = 378 \]

Now we have the values calculated:

• \( 37.8 / 10^1 = 3.78 \)
• \( 37.8 \times 10^2 = 3780 \)
• \( 37.8 / 10^3 = 0.0378 \)
• \( 37.8 / 10^2 = 0.378 \)
• \( 37.8 \times 10^1 = 378 \)

Let's place these values in order from least to greatest:

1. \( 0.0378 \)
2. \( 0.378 \)
3. \( 3.78 \)
4. \( 378 \)
5. \( 3780 \)

In terms of the original expressions, the order is:

• \( 37.8 / 10^3 \)
• \( 37.8 / 10^2 \)
• \( 37.8 / 10^1 \)
• \( 37.8 \times 10^1 \)
• \( 37.8 \times 10^2 \)