Find three rational numbers between 3.1415 and 3.1416.
3.14151, 3.14152, 3.14153
Explanation
The context establishes that there are infinitely many rational numbers between any two points. Since 3.1415 and 3.1416 are terminating decimals, they are rational numbers. To find rational numbers between them, we can simply extend their decimal representations by adding more digits. Rewriting them as 3.14150 and 3.14160 makes it easy to identify the terminating decimals that fall between them, which are also rational numbers.
Solution Steps
Step 1: Recognize that the given numbers, 3.1415 and 3.1416, are terminating decimals, which makes them rational numbers.
Step 2: Rewrite both numbers with an additional decimal place to find values in between. So, 3.1415 becomes 3.14150 and 3.1416 becomes 3.14160.
Step 3: Identify the numbers that lie strictly between 3.14150 and 3.14160. These are 3.14151, 3.14152, 3.14153, 3.14154, 3.14155, 3.14156, 3.14157, 3.14158, and 3.14159.
Step 4: Select any three of these numbers. The three rational numbers between 3.1415 and 3.1416 are 3.14151, 3.14152, and 3.14153.