Rational Numbers between Two Rational Numbers
Rational Numbers between Two Rational Numbers
Rational Numbers between two Rational Numbers:
We will learn to insert rational numbers between two rational numbers. Let us recall integers and properties of various operations on them. We know between two non-consecutive integers x and y there are (x - y - 1) integers. However, there is no integer between two consecutive integers.
For example, between -7 and 7 there are 7 - (-7) - 1 = 7 + 7 - 1 = 14 – 1 = 13 integers. The integers are -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 and 6 but there is no integer between 2 and 3 since they are consecutive integers.
Thus, we find that between two given integers there may or may not lie any integer.
Example: Find out 100 rational numbers lying between -9/19 and 5/19.
Solution:
We have,
-9/19 = -9 × 10/19 × 10 = -90/190 and,
5/19 = 5 × 10/19 × 10 = 50/190
We know that
-90 < -89 < -88 < -87 < -86 < -85 < …….. < -25 < -24 < -23 < -22 < …….. < -1 < 0 < 1 < 2 < …….. < 9 < 10
⇒ -90/190 < -89/190 < -88/190 < -87/190 < -86/190 < -85/190 < …….. < -25/190 < -24/190 < -23/190 < -22/190 < …….. < -1/190 < 0/190 < 1/190 < 2/190 < …….. < 9/190 < 10/190
Hence, < -89/190 < -88/190 < -87/190 < -86/190 < -85/190 < …….. < -25/190 < -24/190 < -23/190 < -22/190 < …….. < -1/190 < 0/190 < 1/190 < 2/190 < …….. < 9/190 < 10/190 are the 100 rational numbers between -9/19 = -90/190 and 5/19 = 50/190.
Choose the rational number which does not lie between rational numbers | |||
| Right Option : C | |||
| View Explanation | |||
A rational number between | |||
| Right Option : D | |||
| View Explanation | |||
A rational number between | |||
| Right Option : D | |||
| View Explanation | |||
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