Using Calculators, we discover that...

Using a calculator,
what values do we get for each of the following

Group 1
(a) 3/8
(b) -9/25

Group 2
(c) 5/9
(d) -9/11

Group 3
(e) 3/14
(f) -2/19

Can you tell any difference amongst the 3 groups of numbers?
Each of them has as "special name". What is it?
Hint: You may refer to your textbook (p45 & p46) or see Hint 1; Hint 2

After note

About the calculators:
  • We learnt that different brands/models of calculators adopt slightly different algorithms when displaying the final answers (for those with decimals, in particular).
  • Method 1: By rounding off the numbers
  • Method 2: By truncation (without taking into consideration the next digit that would not be displayed)
About Numbers:
  • All numbers can be expressed as fractions, hence they are all rational numbers
  • Amongst the rational numbers, there are 3 types: Terminating decimals; Repeating (Recurring) decimals; Non-terminating and non-repeating decimals
  • There are numbers like π that cannot be expressed as a fraction. These are known as irrational numbers

32 comments:

  1. Group 1
    (a) 3/8 = 0.375
    (b) -9/25 = -0.36

    Group 2
    (c) 5/9 = 0.55555556
    (d) -9/11 = 0.81818182

    Group 3
    (e) 3/14 = 0.21428571
    (f) -2/19 = -0.10526316

    ReplyDelete
  2. Group 1
    (a) 3/8 = 0.375
    (b) -9/25= -0.36

    Group 2
    (c) 5/9 = 0.555555555
    (d) -9/11= -0.818181818

    Group 3
    (e) 3/14 = 0.214285714
    (f) -2/19 = -0.105263157

    Teoh Yun

    ReplyDelete
  3. a) 0.375
    b) -0.36
    c) 0.555555555
    d) -0.818181818
    e) 0.214285714
    f) -0.105263157

    ReplyDelete
  4. a) 0.375
    b) -0.36
    c) 0.55555556
    d) -0.81818181812
    e) 0.214857143
    f) -0.1052631579

    Yes.

    Group 1 - Terminating decimal

    Group 2 - repeating decimal

    Group 3 - Unknown. : D

    ReplyDelete
  5. Group 1
    (a)0.375
    (b)0.36
    Group 2
    (a)0.5555555556
    (b)0.8181818182
    Group 3
    (a)0.2142857143
    (b)0.1052631579

    I used natural V.P.A.M calculator

    ReplyDelete
  6. This comment has been removed by the author.

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  7. The group is called the terminating decimal
    (a)0.375
    (b)-0.36
    This group is called the repeating decimal
    (c)0.555555555555
    (d)-0.81818181818
    This group is called the real numbers
    (e)0.214285714
    (f)-0.105263157

    ReplyDelete
  8. Terminating Decimals
    a) 0.375
    b) -0.36
    Repeating decimals
    c) 0.5555555556
    d)-0.8181818182
    not sure
    e) 0.2142857143
    f) -0.1052631579

    ReplyDelete
  9. a) 0.375
    b) -0.36
    c) 0.5555555556
    d) -0.8181818182
    e) 0.2142857143
    f) -0.1052631579

    Group 1: Terminating decimal
    Group 2: Repeating decimal
    Group 3: Yet to be found.....

    ReplyDelete
  10. This comment has been removed by the author.

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  11. Group 1(Terminating Decimal)
    (a) 3/8=0.375
    (b) -9/25=-0.36
    Group 2(Repeating decimal)
    (c) 5/9=0.5555555556
    (d) -9/11=0.8181818182
    Group 3(Non-terminating and non-repeating decimals)
    (e) 3/14=0.2142857143
    (f) -2/19=-0.1052631579

    ReplyDelete
  12. Group 1 (Terminating Decimal)
    a) 0.375
    b) -0.36
    Group 2 (Recurring Decimal)
    c) 0.55555556
    d) -0.81818182
    Group 3 (Irrational Decimal)
    e) 0.21428571
    f) -0.10526316

    ReplyDelete
  13. Group 1
    (a) 3/8 = 0.375
    (b) -9/25 = -0.36

    Group 2
    (c) 5/9 = 0.5555555556
    (d) -9/11 = -0.8181818182

    Group 3
    (e) 3/14 = 0.2142857143
    (f) -2/19 = -0.1052631579

    Group 1 are finite numbers and are called terminating decimals.
    Group 2 are repeating decimals.
    Group 3 are non-terminating and non-repeating decimals.

    ReplyDelete
  14. Question: Answer:

    Group 1 (Terminating Decimals)
    (a) 3/8 (a) 0.375
    (b) -9/25 (b) -0.36

    Group 2 (Recurring Decimals)
    (c) 5/9 (c) 0.555555555
    (d) -9/11 (d) -0.818181818

    Group 3 (Irrational Decimals)
    (e) 3/14 (e) 0.214285714
    (f) -2/19 (f) -0.105263157

    ReplyDelete
  15. Group 1- Terminating Decimal
    (a) 3/8 =0.375
    (b) -9/25=-0.36

    Group 2- Repeating Decimal
    (c) 5/9=5/9 (0.5555555555…)
    (d) -9/11=-9/11 (-0.8181818181…)

    Group 3-Non-Terminating Decimals
    (e) 3/14=3/14 (0.2142857143…)
    (f) -2/19=-2/19 (-0.1052631579…)

    ReplyDelete
  16. Group 1: 0.375 & -0.36
    Group 2: 0.55555555...... & -0.818181818181.............
    Group 3: 0.21428571 & -0.10526316

    Names of Group 1 is Non-repeating and Non-terminating numbers,Group 2 is Recurring decimals,Group 3 is Terminating decimals

    ReplyDelete
  17. Group 1
    (a) 3/8 =0.375
    (b) -9/25 =-0.36

    Group 2
    (c) 5/9 =5/9 (0.5555555555…)
    (d) -9/11 =-9/11 (-0.8181818181…)

    Group 3
    (e) 3/14 =3/14 (0.214285714281754…)
    (f) -2/19 =-2/19 (-0.105263157894737…)

    Group 1 - Group of numbers with a terminating decimal.
    Group 2 - Group of numbers with a repeating decimal that has 2 repeating digits.
    Group 3 - Group of numbers with a non-terminating decimal.

    -Christopher Nah

    ReplyDelete
  18. Group 1
    3÷8=0.375
    -9÷25=-0.36

    Group 2
    5÷9=0.5555555556
    -9÷11=0.8181818182

    Group 3
    3÷14=0.2142857143
    -2÷19=0.1052631579

    ReplyDelete
  19. This comment has been removed by the author.

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  20. These are what is shown on the calculator



    0.375, -0.36(Group 1) Terminating Decimal

    0.5555555556, -0.8181818182 (Group 2) Repeating Decimal

    0.2142857143(3 S.F), -0.1052631579(3 S.F) (Group 3) Real Numbers

    ReplyDelete
  21. Group 1 belongs to terminating decimals
    Group 2 belongs to repeating decimals
    Group 3 belongs to real numbers

    ReplyDelete
  22. I used the dashboard calculator.
    Group 1 belongs to terminating decimals.
    Group 2 belongs to repeating decimals.
    Group 3 belongs to real numbers.

    ReplyDelete
  23. group1 is terminating decimal
    a)0.375
    b)0.36
    Group 2 is repeating decimal
    a)0.5555555556
    b)0.8181818182
    Group 3 is rational no. aproximations
    a)0.2142857143
    b)0.1052631579

    ReplyDelete
  24. The calculator shows...

    Group 1 (Terminating Numbers)

    (a) 3/8 = 0.375

    (b)-9/25 = -0.36

    Group 2 (Repeating Number)

    (c) 5/9 = 0.555555556

    (d) 9/11 = 0.8181818182

    Group 3 (Non-Terminating and Non-Repeating Number)

    (e) 3/14 = 0.2142857143

    (f) -2/19 = 0.1052631579

    ReplyDelete
  25. Group 1 is called terminating decimal as it ends after a few decimal.

    Group 2 is called repeating decimal as it repeats itself forever.

    Group 3 is called real number as it is non-terminating and non-repeating.

    ReplyDelete
  26. Group 1
    (a) 3/8 = 0.375
    (b) -9/25 = -0.36

    Group 2
    (c) 5/9 = 0.5555555556
    (d) -9/11 = -0.8181818182

    Group 3
    (e) 3/14 = 0.2142857143
    (f) -2/19 = -0.1052631579

    Group 1 are called terminating decimals and only has a few decimals behind.
    Group 2 are called repeating decimals and has a lot of similar decimals all the way.
    Group 3 are called non-terminating and non-repeating decimals and does not repeat the decimals all the way.

    ReplyDelete
  27. Group 1- Terminating decimals
    a)0.375
    b)-0.36

    Group 2-Repeating decimals
    c)0.555555555
    d)-0.81818181818

    Group 3- Non-terminating decimals
    e)0.214285714
    f)0.105263157

    Difference: Group 1 terminates at 3 decimals place, Group 2 repeats the numbers, Group 3 never terminates.

    ReplyDelete
  28. This comment has been removed by the author.

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  29. Group 1 is terminating decimal

    (a) 3/8
    decimal is 0.375
    (b) -9/25
    decimal is -0.36

    Group 2 is repeating decimal

    (c) 5/9
    decimal is 0.555555555
    (d) -9/11
    decimal is -0.818181818

    Group 3 is Non-terminating and non-repeating decimals

    (e) 3/14
    decimal is 0.214285714
    (f) -2/19
    decimal is -0.105263157

    ReplyDelete
  30. Group 1
    Terminating Decimal

    Group 2
    Repeating decimal

    Group 3
    Non-terminating decimal

    ReplyDelete
  31. Group 1 : 0.375 & -36 Terminating Decimals
    Group 2 : 0.55555555555... & -0818181... Recurring Decimals
    Group 3 : 0.2142857143 & 0.1052631579 Non-repeating and Non-terminating numbers

    ReplyDelete
  32. group 1
    (a)0.375
    (b)-0.36

    terminating decimals

    group 2
    (c)0.555555555
    (d)-0.818181818

    repeating decimals

    group 3
    (e)0.214285714
    (f)0.105263157

    non-terminating number


    the numbers in group 1(terminating number) has only 2 to 3 decimals,the numbers in group 2(repeating decimals)has recurring numbers and numbers in group 3(non terminating numbers) have no-recurring numbers.

    ReplyDelete