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Polynomials

Question

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Find three rational numbers between 0 and 0.1. Also, find twenty rational numbers between 0 and 0.1.

Solution

0 equals 0 over 1 equals fraction numerator 0 cross times 100 over denominator 1 cross times 100 end fraction equals 0 over 100 0.1 equals 1 over 10 equals fraction numerator 1 cross times 10 over denominator 10 cross times 10 end fraction equals 10 over 100

Thus, three rational numbers between 0 and 0.1 can be taken as

1 over 100 comma space 2 over 100 space space and space 3 over 100. space straight i. straight e. space 0.01 comma space 0.02 space space and space 0.03

Again,

0 equals 0 over 1 equals fraction numerator 0 cross times 1000 over denominator 1 cross times 1000 end fraction equals 0 over 1000 equals 0.1 equals 1 over 10 equals fraction numerator 1 cross times 100 over denominator 10 cross times 100 end fraction equals 100 over 1000

Thus, twenty rational numbers between 0 and 0.1 can be taken as

1 over 1000 space space 2 over 1000 comma space 3 over 1000 comma space 4 over 1000 comma space 5 over 1000 6 over 1000 comma space 7 over 1000 comma space 8 over 1000 comma 9 over 1000 comma 10 over 1000 11 over 1000 comma space 12 over 1000 comma 13 over 1000 comma 14 over 1000 comma space 15 over 1000 comma 16 over 1000 comma 17 over 1000 comma 18 over 1000 comma 19 over 1000 space a n d space 20 over 1000 comma

i.e., 0.001,0.002,0.003,0.004,0.005,0.006,0.007, 0.008,0.009,0.01,0.011,0.012,0.013,0.014,0.015, 0.016,0.017, 0.018, 0.019 and 0.02

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