Question

The value of the irrational number 5x/8


is between which pair of rational numbers?
between 1.96 and 1.97
between 1.97 and 1.98
between 1.98 and 1.99
between 1.99 and 2.00

Answer 1

To determine the value of the irrational number \( \frac{5x}{8} \) and which pair of rational numbers it lies between, we need to know the value of \( x \). However, since \( x \) is unspecified, we can analyze the potential ranges.

1. **Finding decimal values**: If \( x \) is between 1 and 2 (a common assumption for an irrational number), the value of \( \frac{5x}{8} \) would be calculated as follows:

- For \( x = 1 \):
\[
\frac{5(1)}{8} = \frac{5}{8} = 0.625
\]

- For \( x = 2 \):
\[
\frac{5(2)}{8} = \frac{10}{8} = 1.25
\]

So, \( \frac{5x}{8} \) ranges from 0.625 to 1.25 as \( x \) moves from 1 to 2.

2. **If we extend this to larger \( x \)**:
- For \( x = 3 \):
\[
\frac{5(3)}{8} = \frac{15}{8} = 1.875
\]

- For \( x = 4 \):
\[
\frac{5(4)}{8} = \frac{20}{8} = 2.5
\]

Thus, if \( x \) is between 3 and 4, then \( \frac{5x}{8} \) would range from:
- By 3: 1.875
- By 4: 2.5, which offers the range values from \( 1.875 \) to \( 2.5 \).

3. **Identifying the exact pairs**:
- From \( 1.875 \) to \( 2.5 \), the relevant comparisons:
- \( 1.99 \) to \( 2.00 \)
- \( 1.98 \) to \( 1.99 \)

Hence, particularly focused on the first set of rational bounds provided, the value of \( \frac{5x}{8} \) specifically lies between **1.99 and 2.00** for x values ranging between a bit over 3.

Thus the answer is:
- **between 1.99 and 2.00.**