Find two irrational numbers lying between 0.1 and 0.12.
Answers
Answer:
.·. Answers are sqrt(0.011), sqrt(0.012), sqrt(0.013), sqrt(0.014).
Step-by-step explanation:
For irrational number you can write any number
for example you can write answer as 0.1144367867 & 0.10577828292 like this
Rather than this
sprt(0.01) = 0.1
sqrt(0.011) = 0.10488088
sqrt(0.012) = 0.1095445
sqrt(0.013) = 0.11401754
sqrt(0.014) = 0.11832159
sqrt(0.0144) = 0.12
All these are in a range of 0.1 to 0.12
.·. Answers are sqrt(0.011), sqrt(0.012), sqrt(0.013), sqrt(0.014).
Given : Numbers 0.1 and 0.12
Let a = 0.10 and b = 0.12
We observe that the second place of their decimal representations are distinct . Number a has digit 0 and b has digit 2. So, a < b.
So , if we Consider two irrational numbers c = 0.1010010001….. and d = 0.1101001000100001.....
Clearly, c = 0.1010010001….. and d 0.1101001000100001..... are an irrational numbers such that a < c < d < b .
Hence, c (0.1010010001…..) and d (0.1101001000100001.....) are required irrational numbers.
HOPE THIS ANSWER WILL HELP YOU…..
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