1. Example-1
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)`
This material is intended as a summary. Use your textbook for detail explanation.
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