Number of Rational Numbers between two numbers

Transcript

Number of Rational Numbers between two numbers Let’s find some Rational Numbers between 1 & 2 The Gap Between Numbers Let's look at the numbers 1 and 2 on the number line. How many rational numbers (fractions) do you think can fit in the gap between them?Finding the Middle We can find a number right in the middle by taking their average! . We easily squeezed one in. 1 2 Squeezing Another One In at about the smaller gap between 1 and ? Let's take the average again!Getting Crowded! The gap is getting tight, but the number line isn't changing size! Between 1 and , we take the average again: 9/8. 1 2 It Never Ends... We can squeeze another one between 1 and . it's ! Because we aren't zooming in, you can see exactly how closely packed they get.The Answer: Infinitely Many! Because we can repeat this averaging process FOREVER in EVERY gap, there are INFINITELY MANY rational numbers between any two points! The number line gets completely filled.Thus, we can say that Between two rational numbers, there are infinitely many rational numbers