Find six rational numbers between 3 and 4.
Understand the Problem
The question is asking for six rational numbers that lie between the whole numbers 3 and 4. Rational numbers can be represented as fractions or decimals. I will provide examples of such numbers.
Answer
The six rational numbers between 3 and 4 are: $ 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 $.
Answer for screen readers
The six rational numbers between 3 and 4 are:
$$ 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 $$
Steps to Solve
- Identify the range for rational numbers
We need to find rational numbers that lie between the whole numbers 3 and 4. Therefore, our range is:
$$ 3 < x < 4 $$
- Select fractions between 3 and 4
Rational numbers can be expressed as fractions. We can add a fraction to 3 or create fractions with 1 in the numerator and numbers in the denominator. For example, we could try:
$$ 3 + \frac{1}{10}, 3 + \frac{2}{10}, 3 + \frac{3}{10}, \ldots $$
- Calculate specific numbers
By calculating the fractions we can find:
- $ 3 + \frac{1}{10} = 3.1 $
- $ 3 + \frac{2}{10} = 3.2 $
- $ 3 + \frac{3}{10} = 3.3 $
- $ 3 + \frac{4}{10} = 3.4 $
- $ 3 + \frac{5}{10} = 3.5 $
- $ 3 + \frac{6}{10} = 3.6 $
- List the rational numbers
Now, we can list the six rational numbers we found between 3 and 4:
$$ 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 $$
The six rational numbers between 3 and 4 are:
$$ 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 $$
More Information
Rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers. They can also be represented as terminating or repeating decimals. The six examples provided all fall in the decimal format.
Tips
- Choosing numbers outside the range of 3 and 4.
- Confusing rational numbers with irrational numbers, which cannot be expressed as a fraction.
