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  1. Asked: In:

    You know that 1 7 = 0.142857142857142857…. Can you predict what the decimal expansions of 2/7,3/7,4/7,5/7,6/7 are, without actually doing the long division? If so, how?

    rishab17

    Without actual long division, the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are as follows: 2/7 = 2 × 1/7 = 2 × 0.142857142857142857... = 0.285714285714285714... 3/7 = 3 × 1/7 = 3 × 0.142857142857142857... = 0.428571428571428571... 4/7 = 4 × 1/7 = 4 × 0.142857142857142857... = 0.5714285714285714Read more

    Without actual long division, the decimal expansions of 2/7, 3/7, 4/7, 5/7, 6/7 are as follows:
    2/7 = 2 × 1/7 = 2 × 0.142857142857142857… = 0.285714285714285714…
    3/7 = 3 × 1/7 = 3 × 0.142857142857142857… = 0.428571428571428571…
    4/7 = 4 × 1/7 = 4 × 0.142857142857142857… = 0.571428571428571428…
    5/7 = 5 × 1/7 = 5 × 0.142857142857142857… = 0.714285714285714285…
    6/7 = 6 × 1/7 = 6 × 0.142857142857142857… = 0.857142857142857142…

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  2. Asked: In:

    Express the following in the form p/q , where p and q are integers and q ≠ 0.

    rishab17

    (i) 0.666... Let x = 0.666... ⇒ x = 0.6666... ...(i) Multiplying equation (i) by 10 both sides 10x = 6.6666.. ⇒ 10x = 6 + 0.6666... ⇒ 10x = 6 + x [From equation (i)] ⇒ 10x x = 6 ⇒ 9x = 6 ⇒ x = 6/9 = 2/3 (ii) 0.4777... Let x = 0.4777... ⇒ x = 0.47777... ...(i) Multiplying equation (i) by 10 both sideRead more

    (i) 0.666…
    Let x = 0.666…
    ⇒ x = 0.6666… …(i)
    Multiplying equation (i) by 10 both sides
    10x = 6.6666..
    ⇒ 10x = 6 + 0.6666…
    ⇒ 10x = 6 + x [From equation (i)]
    ⇒ 10x x = 6
    ⇒ 9x = 6
    ⇒ x = 6/9 = 2/3
    (ii) 0.4777…
    Let x = 0.4777…
    ⇒ x = 0.47777… …(i)
    Multiplying equation (i) by 10 both sides
    ⇒ 10x = 4.7777… …(ii)
    Multiplying equation (ii) by 10 both sides
    ⇒ 100x = 47.7777…
    ⇒ 100x = 43 + 4.7777…
    ⇒ 100x = 43 + 10x [From equation (ii)]
    ⇒ 100x = 10x = 43
    ⇒ 90x = 43
    ⇒ x = 43/90
    (iii) 0.001001001…
    Let x = 0.001001001…
    ⇒ x = 0.001001001…
    Multiplying equation (i) by 1000 both sides
    1000x = 1.001001001…
    ⇒ 1000x = 1 + 0.001001001…
    ⇒ 1000x = 1 = x [From equation (i)]
    ⇒ 1000x – x = 1
    ⇒ 999x = 1
    ⇒ x = 1/999

    Here is the Video explanation of the above question 😎

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  3. Asked: In:

    Visualise 4.262626… on the number line, using successive magnification.

    rishab17

    => First of all, we observe that 4.2626 (4.262626...) lies between 4 and 5. Divide this portion into 10 equal parts. => In the next step, we locate 4.2626 between 4.2 and 4.3. => To get a more accurate visualisation of representation, we divide this portion of number line into 10 equal partRead more

    => First of all, we observe that 4.2626 (4.262626…) lies between 4 and 5. Divide this portion into 10 equal parts.
    => In the next step, we locate 4.2626 between 4.2 and 4.3.
    => To get a more accurate visualisation of representation, we divide this portion of
    number line into 10 equal parts and use a magnifying glass to visualize that 4.2626
    lies between 4.262 and 4.263.
    => Now to visualise 4.2626 still more accurately, we divide the portion between
    4.262 and 4.263 into 10 equal parts and locate 4.2626.

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  4. Asked: In:

    Classify the following numbers as rational or irrational:

    rishab17

    (i) 2 − √5 Irrational Number (ii) (3 + √23) − √23 Rational Number (iii) 2√7 / 7√7 Rational Number (iv) 1/√2 Irrational Number (v) 2π Irrational Number

    (i) 2 − √5 Irrational Number
    (ii) (3 + √23) − √23 Rational Number
    (iii) 2√7 / 7√7 Rational Number
    (iv) 1/√2 Irrational Number
    (v) 2π Irrational Number

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    • 3
  6. Asked: In:

    It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

    rishab17

    Probability that two students are not having same birthday P (not E) = 0.992 Probability that two students are having same birthday P (E) = 1- P (not E) = 1 - 0.992 = 0.008 Here you can see the explanation video of this above question👇😃

    Probability that two students are not having same birthday P (not E) = 0.992
    Probability that two students are having same birthday P (E) = 1- P (not E) = 1 – 0.992 = 0.008

    Here you can see the explanation video of this above question👇😃

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