List `2/3,sqrt2,0.7,7/4` and 1.5 in order from least to greatest

Options

A. `2/3,0.7,sqrt2,1.5,7/4`
B. `2/3,sqrt2,0.7,7/4,1.5`
C. `2/3,sqrt2,0.7,1.5,7/4`
D. `2/3,0.7,sqrt2,7/4,1.5`

Answer

To list the numbers \( \frac{2}{3}, \sqrt{2}, 0.7, \frac{7}{4}, \) and \( 1.5 \) in order from least to greatest, we will first convert all the fractions and square roots into decimal form. This will make it easier to compare the values.

### Step 1: Convert each number to decimal form

1. **Convert \( \frac{2}{3} \)**:
\[ \frac{2}{3} = 0.6667 \text{ (approximately)} \]

2. **Convert \( \sqrt{2} \)**:
\[ \sqrt{2} \approx 1.414 \]

3. **The decimal \( 0.7 \)** is already in decimal form:
\[ 0.7 = 0.7 \]

4. **Convert \( \frac{7}{4} \)**:
\[ \frac{7}{4} = 1.75 \]

5. **The decimal \( 1.5 \)** is also already in decimal form:
\[ 1.5 = 1.5 \]

### Step 2: List the decimal values

Now we have the following decimal values:
- \( \frac{2}{3} \approx 0.6667 \)
- \( \sqrt{2} \approx 1.414 \)
- \( 0.7 = 0.7 \)
- \( \frac{7}{4} = 1.75 \)
- \( 1.5 = 1.5 \)

### Step 3: Compare the decimal values

Now, we will compare these decimal values:
- \( 0.6667 \) (from \( \frac{2}{3} \))
- \( 0.7 \)
- \( 1.414 \) (from \( \sqrt{2} \))
- \( 1.5 \)
- \( 1.75 \) (from \( \frac{7}{4} \))

### Step 4: Arrange in ascending order

Arranging these values from least to greatest, we get:
1. \( 0.6667 \) (which is \( \frac{2}{3} \))
2. \( 0.7 \)
3. \( 1.414 \) (which is \( \sqrt{2} \))
4. \( 1.5 \)
5. \( 1.75 \) (which is \( \frac{7}{4} \))

### Final Answer

Thus, the numbers in order from least to greatest are:
\[ \frac{2}{3}, 0.7, \sqrt{2}, 1.5, \frac{7}{4} \]

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