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Q.01 - Solve the following and find 3 rational numbers between:

I) [tex]\(\frac{1}{3}\)[/tex] and 12

II) -2 and 0

Sagot :

GinnyAnswer
Certainly! Let's solve the two parts of the question step-by-step.

### Part I: Finding 3 Rational Numbers between [tex]\( \frac{1}{3} \)[/tex] and 12

1. Identify the starting and ending points:
- The starting point is [tex]\( \frac{1}{3} \)[/tex].
- The ending point is 12.

2. Find the total distance between these two points:
- The difference is [tex]\( 12 - \frac{1}{3} \)[/tex].

3. Divide this difference into 4 equal parts to find 3 intermediate values:
- The step size will be [tex]\( \frac{12 - \frac{1}{3}}{4} \)[/tex].

4. Calculate the intermediate rational numbers:
- The first rational number is [tex]\( \frac{1}{3} + \text{step size} \)[/tex].
- The second rational number is [tex]\( \frac{1}{3} + 2 \times \text{step size} \)[/tex].
- The third rational number is [tex]\( \frac{1}{3} + 3 \times \text{step size} \)[/tex].

When we perform these calculations, we get the following rational numbers:
- The first rational number is [tex]\( 3.25 \)[/tex].
- The second rational number is [tex]\( 6.166666666666666 \)[/tex].
- The third rational number is [tex]\( 9.083333333333334 \)[/tex].

### Part II: Finding 3 Rational Numbers between -2 and 0

1. Identify the starting and ending points:
- The starting point is -2.
- The ending point is 0.

2. Find the total distance between these two points:
- The difference is [tex]\( 0 - (-2) \)[/tex].

3. Divide this difference into 4 equal parts to find 3 intermediate values:
- The step size will be [tex]\( \frac{0 - (-2)}{4} \)[/tex].

4. Calculate the intermediate rational numbers:
- The first rational number is [tex]\( -2 + \text{step size} \)[/tex].
- The second rational number is [tex]\( -2 + 2 \times \text{step size} \)[/tex].
- The third rational number is [tex]\( -2 + 3 \times \text{step size} \)[/tex].

When we perform these calculations, we get the following rational numbers:
- The first rational number is [tex]\( -1.5 \)[/tex].
- The second rational number is [tex]\( -1.0 \)[/tex].
- The third rational number is [tex]\( -0.5 \)[/tex].

### Summary

- Three rational numbers between [tex]\( \frac{1}{3} \)[/tex] and 12 are [tex]\( 3.25 \)[/tex], [tex]\( 6.166666666666666 \)[/tex], and [tex]\( 9.083333333333334 \)[/tex].
- Three rational numbers between -2 and 0 are [tex]\( -1.5 \)[/tex], [tex]\( -1.0 \)[/tex], and [tex]\( -0.5 \)[/tex].
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