What Is a Rational Number? - mrscote

Example 1
Writing a Rational Number between Two Given Numbers
Write 3 rational numbers between each pair of numbers.
1 1
1 1
a) 1.25 and 3.26 b) 0.25 and 0.26 c) and d) and
2 4
2 4
A Solution
There are many rational numbers between any two given numbers.
Sketch or visualize a number line in each case.
a) 1.25 and 3.26
Label a number line with integers from 4 to 2.
–3.26 –2.5
0.3 1.25
–4
–3
–2
–1
0
1
2
From the number line, 3 possible rational numbers are:
2.5, 1, and 0.3
b) 0.25 and 0.26
Label a number line with these rational numbers.
Divide the line into 10 equal parts.
–0.259 –0.255 –0.252
–0.26
–0.25
From the number line, 3 possible rational numbers are:
0.252, 0.255, and 0.259
1
c) and
2
1
4
Label a number line from 1 to 1.
Divide the line into quarters.
– 1 4
– 1 8
1
8
–1
– 1 2
0 1 1
1
4 2
From the number line, 3 possible rational numbers are:
1
, 1
, and 1
4 8 8
3.1 What Is a Rational Number? 97