Rational number to fraction and vice versa

1. Our Father who art in Heaven,
Hollowed be Thy Name;
Thy Kingdom come;
Thy will be done,
On Earth as it is in Heaven.
Give us this day our daily bread;
Forgive us our trespasses as we
forgive those who trespass against
us;
And lead us not into temptation
deliver us from evil. Amen.

2. Prepared by:
Ms. Juliet Respicio
MATH DEPARTMENT

3. Expressing Rational Numbers
from Fraction form to Decimal
form and Vice Versa

4. Objectives:
A. Recalls the different properties of operations on integers;
B. Defines rational number;
C. Differentiates the types of rational numbers, fractions and
decimals; and
D. Expresses rational numbers from fraction form to decimal
form and vice versa.

5. Let’s recall! Answer the following questions below.
1. What are the different properties of operations on integers?
 Closure Property
 Commutative Properties
 Associative Properties
 Inverse Properties
 Distributive Property
 Identity Properties
2. Can you identify what property is being illustrated below?
 32 + 4 = 36
 15 (3 + 2) = (15 . 3) + (15 . 2)
 2 + ( 6 + 3 ) = (2 + 6) + 3
 56(1) = 56
 75 + (-75) = 0
 32 ( 14 – 6) = (14 – 6) (32)
Closure Property
Distributive Property of Addition
Associative Property of Addition
Identity Property of Multiplication
Inverse Property of Addition
Commutative Property of Multiplication

6. RATIONAL NUMBERS
A rational number is a number that can be written in the form of
𝑎
𝑏
, where 𝑎
and 𝑏 are integers and 𝑏 ≠ 0.
TYPES OF RATIONAL NUMBERS
 Integers
 Whole Numbers
 Natural Numbers
 Fractions
−3, −2, −1, 0, 1, 2, 3
0, 1, 2, 3, 4, 5
1, 2, 3, 4, 5
2
3
, −
1
4
,
3
5
, −
4
7
Let’s start!

7. TYPES OF FRACTIONS
A proper fraction is a fraction whose numerator is less than the
denominator.
Examples: 2
3
, −
1
4
,
3
5
, −
4
7
,
5
9
An improper fraction is a fraction whose numerator is greater than the
denominator.
Examples:
7
5
, −
23
4
,
3
2
, −
9
2
,
15
4

8. TYPES OF FRACTIONS
A mixed number is a combination of a number and a proper fraction.
Examples:
10
2
3
, −11
1
4
, 8
3
5
, −3
4
7
, 1
5
9
TYPES OF DECIMALS
Terminating decimals are decimal numbers with specific number of
digits after the decimal point.
Examples:
0.756 seven hundred fifty-six thousandths
321.52 three hundred twenty-one and fifty-two hundredths

9. TYPES OF DECIMALS
 Terminating Decimals
Example 90.0075 ninety and seventy-five ten thousandths
Non-terminating decimals are decimal numbers without a specific
number of digits after the decimal point. There are two types of non-
terminating decimals namely:
 Repeating Decimals
1. 0.33 … Is a non-terminating repeating decimal, the repeating digit is 3.
We can also write it as 0.3. The bar above is called vinculum.
2. 0.4242 … Is a non-terminating repeating decimal, the repeating digits is
42. We can also write it as 0.42.

10.  Non-repeating Decimals
Examples:
1. The value 𝜋 is a non-terminating and non-repeating decimal wherein the
approximate value is 3.145926535897932…
2. 5. 14253678594…
3. 17. 90132845367…

11. Fractions to Decimals
Examples:
4
5
= 0.8
200
0
2. )
24
50
= 50 24.00
0.48
0
240
400
400
24
50
= 0.48
0
3. )
38
100
= 100 38.00
0.38
0
380
300
800
800
38
100
= 0.38
1. )
4
5
= 5 4
0.8
0
40
40
0
. 0

12. Fractions to Repeating Decimals
Examples:
1. )
7
9
= 9 7.00
0.77
0
70
63
70
63
7
7
9
= 0.7
2. )
3
11
= 11 3.0000
0.2727
0
30
22
80
77
30
22
80
77
3
3
11
= 0.27

13. Decimals to Fractions
Examples:
To change decimals to fractions, write the decimal number over its
place value. However this is applicable only to terminating and
repeating decimals.
1. 0.4 tenths
=
4
10
=
2
5
0.4 =
2
5
2. 0.025 thousandths
=
25
1000
=
1
40
0.025 =
1
40
3. 2.74 hundredths
= 2
74
100
= 2
37
50
reduce reduce reduce
2.74 = 2
37
50

14. To change repeating decimals to fractions, use the formula
𝑁
𝑃𝑉−1
, where N
is the decimal number and PV is the place value of decimal.
Examples:
1. 0.8 =
𝑁
𝑃𝑉 − 1
=
8
10 − 1
=
8
9
0.8 =
8
9
2. 0.123=
𝑁
𝑃𝑉 − 1
=
123
1000 − 1
=
123
999
=
123
999
=
41
333 0.123 =
41
333
Repeating Decimals to Fractions

15. 0.25 =
25
99
=
𝑁
𝑃𝑉 − 1
5.42 = 5
14
3
4. 5.42
= 5
42
100 − 1
= 5
42
99
= 5
14
33
reduce
Repeating Decimals to Fractions
3. 0.25 =
𝑁
𝑃𝑉 − 1
=
25
100 − 1
=
25
99

16. A. Express the following
fractions as decimals:
1.
2
9
5.
5
12
2.
3
4
3.
1
25
4.
6
5
B. Write the equivalent fraction
form of the following decimals:
6. - 5.69
7. 0.416
8. 0.250
9. 1.25
10. 0.35
ASSESSMENT
Note: Show your solution for 5 points each.

17. ASSIGNMENT
Research and study in advance, operations on
rational numbers, in preparation for our next
topic next week.

18. Glory be to the Father, and
to the Son, and to the Holy
Spirit. As it was in the
beginning, is now, and ever
shall be, world without end.
Amen.

19. THANK YOU
AND
GOD BLESS!!