NCERT Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.3
Question 1.
Write the following in decimal form and say what kind of decimal expansion each has
Solution:
Question 2.
You know that
Solution:
Question 3.
Express the following in the form
(i) 0.
(ii) 0.4
(iii) 0.
Solution:
(i)Let x= 0.
Multiplying Eq. (i) by 10, we get
10x = 6.666.. ….(ii)
On subtracting Eq. (ii) from Eq. (i), we get
(10x- x)=(6.666…) – (0.666…)
9x = 6
x= 6/9
⇒ x=2/3
(ii) Let x = 0.4
Multiplying Eq. (iii) by 10. we get
10x = 4.777… . …(iv)
Multiptying Eq. (iv) by 10, we get
100x = 47.777 ….. (v)
On subtracting Eq. (v) from Eq. (iv), we get
(100 x – 10x)=(47.777….)-(4.777…)
90x =43
⇒ x =
(iii) Let x = 0.
Multiplying Eq. (vi) by (1000), we get
1000x = 1.001001001… .. .(vii)
On subtracting Eq. (vii) by Eq. (vi), we get
(1000x—x)=(1.001001001….) – (0.001001001……)
999x = 1
⇒ x =
Question 4.
Express 0.99999… in the form
Solution:
Let x = 0.99999… ………..(i)
Multiplying Eq. (i) by 10, we get
10x = 9.99999… …(ii)
On subtracting Eq. (ii) by Eq. (i), we get
(10 x – x) = (9.99999..) – (0.99999…)
9x = 9
⇒ x =
x = 1
Question 5.
What can the maximum number of digits be in the repeating block of digits in the decimal expansion of
Solution:
The maximum number of digits in the repeating block of digits in the decimal expansion of
Thus,
Question 6.
Look at several examples of rational numbers in the form
Solution:
Consider many rational numbers in the form
Let the various such rational numbers be
In all cases, we think of the natural number which when multiplied by their respective denominators gives 10 or a power of 10.
From the above, we find that the decimal expansion of above numbers are terminating. Along with we see that the denominator of above numbers are in the form 2m x 5n, where m and n are natural numbers. So, the decimal representation of rational numbers can be represented as a terminating decimal.
Question 7.
Write three numbers whose decimal expansions are non-terminating non-recurring.
Solution:
0.74074007400074000074…
0.6650665006650006650000…
0.70700700070000…
Question 8.
Find three different irrational numbers between the rational numbers
Solution:
To find irrational numbers, firstly we shall divide 5 by 7 and 9 by 11,
so,
Question 9.
Classify the following numbers as rational or irrational
Solution:
(i)
(ii)
(iii) 0.3796 = rational (terminating.)
(iv) 7.478478… =7.
(v) 1.101001000100001… = irrational (non-terminating non-repeating.)
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