Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 28
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36MODULE -
1
Number Systems
Algebra
Solution:
Consider the number
2×
3
We know that 6 approximately equals 2.45.
Notes
∴ It lies between 2 and 3 and it is an irrational number.
Example 1.20:
Find an irrational number lying between 3 and 2.
3 +
2
Solution:
Consider the number
2
3
. 1
732
=
+
≈
+
=
1
1
. 1
866
2
2
3 +
2
∴
≈ 1.866 lies betwen 3 (≈ 1.732) and 2
2
3 +
2
∴ The required irrational number is
2
CHECK YOUR PROGRESS 1.6
1. Find an irrational number between the following pairs of numbers
(i) 2 and 4
(ii) 3 and 3
(iii) 2 and 3
2. Can you state the number of irrationals between 1 and 2? Illustrate with three examples.
1.13 ROUNDING OFF NUMBERS TO A GIVEN NUMBER
OF DECIMAL PLACES
It is sometimes convenient to write the approximate value of a real number upto a desired
number of decimal places. Let us illustrate it by examples.
Example 1.21:
Express 2.71832 approximately by rounding it off to two places of
decimals.
Solution:
We look up at the third place after the decimal point. In this case it 8, which is
more than 5. So the approximate value of 2.71832, upto two places of decimal is 2.72.
Example 1.22:
Find the approximate value of 12.78962 correct upto 3 places of decimals.
30
Mathematics Secondary Course
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