### 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 consist of examples of terminating decimals.
Group 2 consist of examples of repeating decimals.

2. Group 1
a. 0.375
b. -0.36

Group 2
recurring decimal:

c. 0.5555555555556

d. -0.818181818182

Group 3

e. 0.2142857143

f. -0.1052631579

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4. Group 1
a) 3/8 = 0.275
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 = 0.1052632579

Group 1 is a terminating decimal
Group 2 is a repeating decimal
Group 3 is a non-terminating or repeating decimal

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7. a)0.375
b)-0.36
c)0.5555555555
d)-0.818181818
e)0.214285714
f)-0.105263157

8. Group 1
(a) 0.375
(b) -0.36

Group 2 (recurring decimals)
(c) 0.5555555556
(d) 0.8181818182

Group 3
(e) 0.2142857143
(f) -0.1052631579

9. Group 1
(a) 3/8 = 0.275
(b) -9/25 = -0.36

Numbers from group 1 are terminating decimal

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

Numbers from group 2 are repeating decimal

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

Numbers from group 3 are non-repeating decimal and non-terminating deciaml

10. Group 1
(a) 3/8= 0.375
(b) -9/25= -0.36
Group 2
(a) 5/9= 0.5555555556
(b) -9/11= 0.8181818182
Group 3
(a) 3/14= 0.2142857142
(b) -0.1052631579

Group 1 is terminating decimals.
Group 2 is repeating decimals.
Group 3 is non-terminating decimals.

JJ(:

11. Group 1
(a) 0.375
(b)-0.36

Group 2
(c)0.5555555556
(d)-0.8181818182

Group 3
(e)0.2142857143
(f)-0.1052631579

Group 1 is a terminating decimal
Group 2 is a repeating decimal
Group 3 is a non-terminating decimal

12. Group 1 a) 0.375
b) -0.36
Group 2 a) 0.5555555556
b) -0.8181818182
Group 3 e) 0.2142857143
f) -0.1052631579

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14. Group 1
a0.375
b -0.36
Group 2
c0.5555555555
d0.8181818182
Group 3
e0.2142857143
f -0.1052631579

15. (a) 0.375
(b) -0.36
(c) 0.5555555556
(d) -0.8181818182
(e) 0.2142857143
(f) -0.1052631579

Group 1 examples are terminating decimals.
Group 2 examples are repeating decimals.
Group 3 examples are neither terminating nor repeating decimals.

16. 3/8=0.375
-9/25=-0.36

Group 1 consists of terminating decimals.

5/9=0.5555555556
-9/11=0.8181818182

Group 2 consists of repeating decimals.

3/14=0.2142857143
-2/19=-0.1052631579

Group 3 consists of repeating decimals.

17. Group 1 are examples of terminating decimals
a)0.375

b)0.36
Group 2 are examples of recurring decimals

c)0.555555555

d)-0.818181818

Group 3 are examples of repeating decimals

e)0.214285714

f)-0.105263157

18. 1.(a)0.375
1.(b)-0.36
2.(a)0.555555555...
2.(b)0.818181818...
3.(a)0.214285714...
3.(b)0.105263157...

Group 1 consist of terminating decimals.
Group 2 consist of repeating decimals.
Group 3 consist of non-terminating and non-repeating decimals.

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

Group 2
(c) 5/9 = 0.555555556...
(d) -9/11 = -0.81818182

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

The fractions in Group 1 are examples of terminating decimals as they have a finite number of digits.

The fraction in Group 2, on the other hand, are repeating decimals.

The fractions in Group 3 have infinite number yet they are not repeating. They are neither terminating nor repeating numbers.

20. group 1
(a) 0.375
(b)-0.35

these are terminating decimal

Group 2
(c) 0.5555555556
(d)-0.8181818182

these are repeating decimals

group 3

(e) 0.2142857143
(f)-0.1052631579

these are also repeating decimals

21. Group 1:
(a)0.375
(b)-0.36
Group 2:
(c)0.5555555556
(d)0.818181818182
Group 3:
(e)0.2142857143
(f)-0.1052631579
Group 1 is terminating decimal.
Group 2 is repeating decimal.
Group 3 is non-terminating decimal.

22. Group 1
a) 0.375
b) -0.36

Group 2
c) 0.555555555
d) 0.818181818

Group 3
e) 0.214285714
f) -0.105263157

terminating decimals and repeating decimals.

23. Group 1:
(a) 0.375
(b) -0.36

Group 2:
(c) 0.555555555
(d) -0.818181818

Group 3:
(e) 0.214285714
(f) 0.105263157

Group 1 is terminating decimal.
Group 2 is repeating decimal.
Group 3 is non-terminating decimal.

24. Numbers in group 1 consist of decimals which do not go on and on forever.
Numbers in group 2 and 3 consist of numbers which go on and on forever .
(a) 0.375
(b) -0.36
(c) 0.5555555556
(d) -0.8181818182
(e) 0.2142857143
(f) -0.1052631579

25. Group 1 : 3/8 = 0.375
-9/25 = -0.36
Numbers in Group 1 consist of decimals which do not repeat themselves over and over.

Group 2 : 5/9 = 0.555555555
-9/11 = 0.818181818
Numbers in Group 2 consist of decimals which repeat themselves.

Group 3 : 3/14 = 0.214285714
-2/19 = -0.105263157
Numbers in Group 3 consist of decimals which goes on and on.

26. group 1
(a)0.375
(b)-0.36
group 2
(c)0.5555555555556
(d)-0.818181818181818
group 3
(e)0.214285714285714
(f)-0.105263157894737
Group 1 is a terminating decimal
Group 2 is a repeating decimal
Group 3 is a non-terminating or repeating decimal