To find two rational numbers between 0.1 and 0.3, follow these steps:
1. Understand the Problem:
- We need to find rational numbers, which are numbers that can be expressed as a fraction of two integers.
- The given interval is between 0.1 and 0.3.
2. Convert Decimal to Fraction:
- The number 0.1 can be expressed as the fraction [tex]\( \frac{1}{10} \)[/tex].
- The number 0.3 can be expressed as the fraction [tex]\( \frac{3}{10} \)[/tex].
3. Identify Rational Numbers Between the Given Bounds:
- Any number between [tex]\( \frac{1}{10} \)[/tex] and [tex]\( \frac{3}{10} \)[/tex] will work, given that it can be expressed as a fraction of two integers.
4. Choose Specific Rational Numbers:
- Let’s select rational numbers that are simple fractions:
- [tex]\( \frac{1}{5} \)[/tex] can be chosen. Note that:
[tex]\[
\frac{1}{5} = 0.2
\][/tex]
which is between 0.1 and 0.3.
- Another rational number that is between [tex]\( 0.1 \)[/tex] and [tex]\( 0.3 \)[/tex] can be [tex]\( \frac{1}{4} \)[/tex]. Note that:
[tex]\[
\frac{1}{4} = 0.25
\][/tex]
which is also between 0.1 and 0.3.
5. Verify Both Numbers:
- [tex]\( \frac{1}{5} = 0.2 \)[/tex], and 0.2 is indeed between 0.1 and 0.3.
- [tex]\( \frac{1}{4} = 0.25 \)[/tex], and 0.25 is indeed between 0.1 and 0.3.
Thus, two rational numbers between 0.1 and 0.3 are 0.2 and 0.25.
