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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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    • 1
  7. Asked: In:

    A bag contains 3 red balls and 5 black balls. A ball is drawn at random from the bag. What is the probability that the ball drawn is (i ) red ? (ii) not red?

    rishab17

    (i) Total number of balls in the bag = 8 Probability of getting a red ball = (Number of favorable outcomes)/(Number of total possible outcomes) = 3/8 (ii) Probability of not getting red ball = 1 Probability of getting a red ball = 1 - 3/8 = 5/8

    (i) Total number of balls in the bag = 8
    Probability of getting a red ball = (Number of favorable outcomes)/(Number of total possible outcomes) = 3/8
    (ii) Probability of not getting red ball = 1
    Probability of getting a red ball = 1 – 3/8 = 5/8

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  8. Asked: In:

    A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (i) red ? (ii) white? (iii) not green?

    rishab17

    Total number of marbles = 5 + 8 + 4 = 17 (i) Number of red marbles = 5 Probability of getting a red marble = (Number of favorable outcomes)/Number of total possible outcomes) = 5/17 (ii) Number of white marbles = 8 Probability of getting a white marble = (Number of favorable outcomes)/Number of totaRead more

    Total number of marbles = 5 + 8 + 4 = 17
    (i) Number of red marbles = 5
    Probability of getting a red marble = (Number of favorable outcomes)/Number of total possible outcomes) = 5/17
    (ii) Number of white marbles = 8
    Probability of getting a white marble = (Number of favorable outcomes)/Number of total possible outcomes) = 8/17
    (iii) Number of green marbles = 4
    Probability of getting a green marble = (Number of favorable outcomes)/Number of total possible outcomes) = 4/17
    Probability of not getting a green marble = 1 – 4/17 = 13/17

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  9. Asked: In:

    A piggy bank contains hundred 50p coins, fifty 1 coins, twenty 2 coins and ten 5 coins. If it is equally likely that one of the coins will fall out when the bank is turned upside down, what is the probability that the coin (i) will be a 50 p coin ? (ii) will not be a ` 5 coin?

    rishab17

    Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180 (i) Number of 50 p coins = 100 Probability of getting a 50 paise coin = (Number of favorable outcomes)/(Number of total possible outcomes) = 100/180 = 5/9 (ii) Number of ₹ 5 coins = 10 Probability of getting ₹ 5 coin = (Number of favorRead more

    Total number of coins in a piggy bank = 100 + 50 + 20 + 10 = 180
    (i) Number of 50 p coins = 100
    Probability of getting a 50 paise coin = (Number of favorable outcomes)/(Number of total possible outcomes) = 100/180 = 5/9
    (ii) Number of ₹ 5 coins = 10
    Probability of getting ₹ 5 coin = (Number of favorable outcomes)/(Number of total possible outcomes) = 10/180 = 1/18
    Probability of not getting a ₹ 5 = 1 – 1/18 = 17/18

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  11. Asked: In:

    Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish What is the probability that the fish taken out is a male fish?

    rishab17

    Total number of fishes in a tank = Number of male fishes + Number of female fishes = 5 + 8 = 13 Probability of getting a male fish = (Number of favorable outcomes)/(Number of total possible outcomes) = 5/13

    Total number of fishes in a tank
    = Number of male fishes + Number of female fishes = 5 + 8 = 13
    Probability of getting a male fish = (Number of favorable outcomes)/(Number of total possible outcomes) = 5/13

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  12. Asked: In:

    A game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8 and these are equally likely outcomes. What is the probability that it will point at

    rishab17

    Total number of possible outcomes = 8 (i) Probability of getting 8 = (Number of favorable outcomes)/(Number of total possible outcomes) = 1/8 (ii) Total number of odd numbers on spinner = 4 Probability of getting an odd number = (Number of favorable outcomes)/(Number of total possible outcomes) = 4/Read more

    Total number of possible outcomes = 8
    (i) Probability of getting 8 = (Number of favorable outcomes)/(Number of total possible outcomes) = 1/8
    (ii) Total number of odd numbers on spinner = 4
    Probability of getting an odd number = (Number of favorable outcomes)/(Number of total possible outcomes) = 4/8 = 1/2
    (iii) The numbers greater than 2 are 3, 4,5, 6, 7, and 8. Therefore, total numbers greater than 2 = 6
    Probability of getting number greater than 2 = (Number of favorable outcomes)/(Number of total possible outcomes) = 6/8 = 3/4
    (iv) The numbers less than 9 are 1, 2, 3, 4, 6, 7, and 8.
    Therefore, total numbers less than 9 = 8
    Probability of gettinga number less than 9 = 8/8 = 1

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