Question

convert 0.7 (theres a bar over 7) to a fraction.

Answer 1

which of the following is an irrational number between 4 and 8?
1. square root of 12
2. square root of 5
3. square root of 8
4. square root of 17

Answer 2

Which of the following rational numbers is not between the square root of 3 and the square root of 6
1. 1.8
2. the square root of 4
3. 1.5
4. 2

Answer 3

To convert the repeating decimal \(0.7\overline{7}\) to a fraction, follow these steps:

1. Let \(x = 0.7\overline{7}\).

2. To eliminate the repeating part, multiply \(x\) by 10 (which shifts the decimal point one place to the right):
\[
10x = 7.7\overline{7}
\]

3. Now, subtract the original \(x\) from this equation:
\[
10x - x = 7.7\overline{7} - 0.7\overline{7}
\]
Simplifying this gives:
\[
9x = 7
\]

4. Now, solve for \(x\):
\[
x = \frac{7}{9}
\]

Thus, \(0.7\overline{7}\) as a fraction is \(\frac{7}{9}\).

Answer 4

To determine which of the given options is an irrational number between 4 and 8, we can evaluate each one:

1. **Square root of 12**:
\[
\sqrt{12} \approx 3.46 \quad \text{(not between 4 and 8, and is irrational)}
\]

2. **Square root of 5**:
\[
\sqrt{5} \approx 2.24 \quad \text{(not between 4 and 8, and is irrational)}
\]

3. **Square root of 8**:
\[
\sqrt{8} = 2\sqrt{2} \approx 2.83 \quad \text{(not between 4 and 8, and is irrational)}
\]

4. **Square root of 17**:
\[
\sqrt{17} \approx 4.12 \quad \text{(between 4 and 8, and is irrational)}
\]

Among the options provided, **\(\sqrt{17}\)** is the only irrational number that falls within the range of 4 and 8.

Answer 5

To determine which of the given rational numbers is not between \(\sqrt{3}\) and \(\sqrt{6}\), we first need to find approximate values for \(\sqrt{3}\) and \(\sqrt{6}\):

- **Calculate \(\sqrt{3}\)**:
\[
\sqrt{3} \approx 1.732
\]

- **Calculate \(\sqrt{6}\)**:
\[
\sqrt{6} \approx 2.449
\]

Now we can establish the interval:
- \(\sqrt{3} \approx 1.732\)
- \(\sqrt{6} \approx 2.449\)

The rational numbers we need to evaluate are:

1. **1.8**:
\[
1.732 < 1.8 < 2.449 \quad \text{(between)}
\]

2. **\(\sqrt{4}\)**:
\[
\sqrt{4} = 2 \quad \text{(between)}
\]

3. **1.5**:
\[
1.5 < 1.732 \quad \text{(not between)}
\]

4. **2**:
\[
1.732 < 2 < 2.449 \quad \text{(between)}
\]

The only number from the list that is **not** between \(\sqrt{3}\) and \(\sqrt{6}\) is **1.5**.