### 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

• 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)
• 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

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

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

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

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

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

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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

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

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.....

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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

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

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.

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

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…)

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

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

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

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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

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

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

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

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

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.

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.

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.

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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

30. Group 1
Terminating Decimal

Group 2
Repeating decimal

Group 3
Non-terminating decimal

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

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.