1. Find Convert Decimal to Fraction of `0.75`

Solution:
`0.75 = 75/100=(75 -: 25)/(100 -: 25)=3/4`

Step by step solution :
Step-1 : write the decimal number as a fraction (by dividing 1)
`0.75=0.75/1`

Step-2 : To eliminate 2 decimal places, multiply both numerator and denominator by `10^2=100`

`0.75/1 xx 100/100=75/100`

Step-3 : Find the Greatest Common Factor (GCF) of `75` and `100`, and reduce the fraction by dividing both numerator and denominator by GCF = 25

`=(75 -: 25)/(100 -: 25)=3/4`

So `0.75 = 3/4`

---

2. Find Convert Decimal to Fraction of `0.5`

Solution:
`0.5 = 5/10=(5 -: 5)/(10 -: 5)=1/2`

Step by step solution :
Step-1 : write the decimal number as a fraction (by dividing 1)
`0.5=0.5/1`

Step-2 : To eliminate 1 decimal places, multiply both numerator and denominator by `10^1=10`

`0.5/1 xx 10/10=5/10`

Step-3 : Find the Greatest Common Factor (GCF) of `5` and `10`, and reduce the fraction by dividing both numerator and denominator by GCF = 5

`=(5 -: 5)/(10 -: 5)=1/2`

So `0.5 = 1/2`

---

3. Find Convert Decimal to Fraction of `1.5`

Solution:
`1.5 = 15/10=(15 -: 5)/(10 -: 5)=3/2=1 (1)/(2)`

Step by step solution :
Step-1 : write the decimal number as a fraction (by dividing 1)
`1.5=1.5/1`

Step-2 : To eliminate 1 decimal places, multiply both numerator and denominator by `10^1=10`

`1.5/1 xx 10/10=15/10`

Step-3 : Find the Greatest Common Factor (GCF) of `15` and `10`, and reduce the fraction by dividing both numerator and denominator by GCF = 5

`=(15 -: 5)/(10 -: 5)=3/2`

Step-4 : Simplify the improper fraction
`3/2 = 1 (1)/(2)`

So `1.5 = 1 (1)/(2)`

---

4. Find Convert Decimal to Fraction of `3.33333...`

Solution:
1. Convert a Repeating Decimal to a Fraction

`3.33333...=3.33...` (Repeating Decimal part is 3)

`3.33... = 3 (1)/(3)`

Step by step solution :
Step-1 : let `x` equals the decimal number

`x = 3.33... ->(1)`

Step-2 : Here repeating digits is 1, So create a second equation by multiplying both sides by `10^1 = 10`

`10 x = 33.333... ->(2)`

Subtract equation (1) from equation (2)

`10 x`	=	`33.333...`
`x`	=	`3.33...`
`9 x`	=	`30`

`:. x = 30/9`


Step-3 : Find the Greatest Common Factor (GCF) of `30` and `9`, and reduce the fraction by dividing both numerator and denominator by GCF = 3

`=(30 -: 3)/(9 -: 3)=10/3`

Step-4 : Simplify the improper fraction
`10/3 = 3 (1)/(3)`

So `3.33... = 3 (1)/(3)`

---

2. Convert a Decimal to a Fraction (Non Repeating)

`3.33333 = 333333/100000`

Step by step solution :
Step-1 : write the decimal number as a fraction (by dividing 1)
`3.33333=3.33333/1`

Step-2 : To eliminate 5 decimal places, multiply both numerator and denominator by `10^5=100000`

`3.33333/1 xx 100000/100000=333333/100000`

Step-3 : Simplify the improper fraction
`333333/100000 = 3 (33333)/(100000)`

So `3.33333 = 3 (33333)/(100000)`

---

---