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  1. Asked: In:

    Express 0.99999 …. in the form p/q. Are you surprised by your answer? With your teacher and classmates discuss why the answer makes sense.

    Rocky Singh

    0.99999... Let x = 0.99999 ... ...(i) Multiplying equation (i) by 10 both sides ⇒ 10x = 9.99999... ⇒ 10x = 9 + 0.99999... ... ⇒ 10x = 9 + x [From equation (i)] ⇒ 10x - x = 9 ⇒ 9x = 9 ⇒ x = 9/9 = 1 The answer makes sense as 0.99999... is very close to 1, that is why we can say that 0.99999 = 1.

    0.99999…
    Let x = 0.99999 … …(i)
    Multiplying equation (i) by 10 both sides
    ⇒ 10x = 9.99999…
    ⇒ 10x = 9 + 0.99999… …
    ⇒ 10x = 9 + x [From equation (i)]
    ⇒ 10x – x = 9
    ⇒ 9x = 9
    ⇒ x = 9/9 = 1
    The answer makes sense as 0.99999… is very close to 1, that is why we can say that 0.99999 = 1.

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  2. Asked: In:

    What can the maximum number of digits be in the repeating block of digits in the decimal expansion of 1/17 ? Perform the division to check your answer.

    Rocky Singh

    The maximum number of digits that can be in the repeating block of digits in the decimal expansion of 1/17 is 16 (less than 17). By performing the actual division, we get 1/17 = 0.058823529411764705882352941176470588235294117647... So, the maximum number of digits that can be in the repeating blockRead more

    The maximum number of digits that can be in the repeating block of digits in the decimal expansion of 1/17 is 16 (less than 17).
    By performing the actual division, we get
    1/17 = 0.058823529411764705882352941176470588235294117647…
    So, the maximum number of digits that can be in the repeating block of digits in the decimal expansion of 1/17 is 16.

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  3. Asked: In:

    Look at several examples of rational numbers in the form p/q (q ≠0), where p and q are integers with no common factors other than 1 and having terminating decimal representations (expansions). Can you guess what property q must satisfy?

    Rocky Singh

    2/5 = 0.4, 1/10 = 0.1, 3/2 = 1.5, 7/8 = 0.875 The denominator of all the rational numbers are in the form of 2ᵐ x 5ⁿ, where m and n are integers.

    2/5 = 0.4, 1/10 = 0.1, 3/2 = 1.5, 7/8 = 0.875
    The denominator of all the rational numbers are in the form of 2ᵐ x 5ⁿ, where m and n are integers.

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  4. Asked: In:

    Write three numbers whose decimal expansions are non-terminating non-recurring.

    Rocky Singh

    Three non-terminating non-recurring decimals: 1) 0.414114111411114 .. 2) 2.01001000100001.. 3) π = 3.1416 ..

    Three non-terminating non-recurring decimals:
    1) 0.414114111411114 ..
    2) 2.01001000100001..
    3) π = 3.1416 ..

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  6. Asked: In:

    The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

    Rocky Singh

    From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 - 5000. Therefore, modal class = 4000 5000 Lower limit () of modal class = 4000 Frequency (f₁) of modal class = 18B Frequency (f₀) of class preceding modal class = 4 Frequency (f₂) of claRead more

    From the given data, it can be observed that the maximum class frequency is 18, belonging to class interval 4000 – 5000.
    Therefore, modal class = 4000 5000
    Lower limit () of modal class = 4000
    Frequency (f₁) of modal class = 18B
    Frequency (f₀) of class preceding modal class = 4
    Frequency (f₂) of class succeeding modal class = 9
    Class size (h) = 1000
    Mode = l + ((f₁ – f₀)/(2f₁ – f₀ – f₂)) × h = 4000 + ((18 – 4)/(2 × 18 – 4 – 9)) × 1000 = 4000 + 608.695 = 4608.695
    Therefore, mode of the given data is 4608.7 runs

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