write down the decimal expansions of those rational numbers in question 39 above which have terminating decimal expansions
Answers
Answer:
The terminating decimal expansion means that the decimal representation or expansion terminates after a certain number of digits. A rational number is terminating if it can be expressed in the form: p / q where q is of the form 2n × 5m.
The rational numbers 13/3125, 17/8, 15/1600, 23/2352, 6/15, and 35/50 have a terminating decimal expansion whereas, 64/455, 29/343, 129/225775, and 77/210 have a non-terminating repeating decimal expansion.
(i) 13/3125 = 0.00416
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
(ii) 17/8 = 2.125
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
(iv) 15/1600 = 0.009375
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
(vi) 23/ (23 × 52) = 23/200 = 0.115
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
(viii) 6/15 = (2 × 3)/(3 × 5) = 2/5 = 0.4
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
(ix) 35/50 = 0.7
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
☛ Check: NCERT Solutions for Class 10 Maths Chapter 1
Video Solution:
Write down the decimal expansions of those rational numbers in Question 1 above which have terminating decimal expansions
NCERT Solutions Class 10 Maths Chapter 1 Exercise 1.4 Question 2
Summary:
The terminating decimal expansion of the rational numbers 13/3125, 17/8, 15/1600, 23/2352, 6/15 and 35/50 are 0.00416, 2.125, 0.009375, 0.115, 0.4 and 0.7 respectively.
☛ Related Questions:
Prove that 3 + 2√5 is irrational.
Prove that the following are irrationals: (i) 1/√2 (ii) 7√5 (iii) 6 + √2
Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion: (i) 13/3125 (ii) 17/8 (iii) 64/455 (iv) 15/1600 (v) 29/343 (vi) 23/2352 (vii) 129/225775 (viii) 6/15 (ix) 35/50 (x) 77/210
The following real numbers have decimal expansions as given below. In each case, decide whether they are rational or not. If they are rational, and of the form p/q, what can you say about the prime factor of q? (i) 43.123456789 (ii) 0.120120012000120000.... (iii) 43.123456789
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