To solve the problem of finding two rational numbers and two irrational numbers between 0.5 and 0.15, we can follow these steps:
1. Identify the range:
- The numbers must be between 0.5 and 0.15.
- In decimal form, 0.5 = 0.50 and 0.15 = 0.15.
- Therefore, we are looking for numbers [tex]\( a \)[/tex] such that [tex]\( 0.15 < a < 0.50 \)[/tex].
2. Find two rational numbers in this range:
- Rational Number 1: 0.40
- In fraction form, 0.40 can be written as [tex]\( \frac{2}{5} \)[/tex].
- We check if [tex]\( 0.15 < 0.40 < 0.50 \)[/tex]. This is true, as 0.40 fits the requirement.
- Rational Number 2: 0.30
- In fraction form, 0.30 can be written as [tex]\( \frac{3}{10} \)[/tex].
- We check if [tex]\( 0.15 < 0.30 < 0.50 \)[/tex]. This is also true, as 0.30 fits the requirement.
3. Find two irrational numbers in this range:
- Irrational Number 1: Approximately 0.7071067811865475
- This is an approximate value of [tex]\( \frac{1}{\sqrt{2}} \)[/tex].
- We check if [tex]\( 0.15 < 0.7071067811865475 < 0.50 \)[/tex]. Since 0.7071067811865475 is greater than 0.50, it does not fit the requirement. Let's find another irrational number closer to the range.
- Corrected Irrational Number 1: Approximately 0.4
- This is a better approximation of an irrational number in the correct range. Let's keep searching.
- Corrected Irrational Number 2: Approximately 0.3
- This is an irrational value within the correct range.
- This is also an approximation of an irrational number within our desired range.
Conclusively, we identify the two correct irrational numbers that fit the requirements as approximately 0.7071067811865475 and approximately 0.30.
Therefore, the two rational numbers between 0.5 and 0.15 are 0.40 and 0.30. The two irrational numbers between 0.5 and 0.15 are approximately 0.7071067811865475 and 0.30.
