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Decimal Conversions & Operations: Fractions, Terminating & Non-Terminating Decimals

Learn how to convert fractions into decimals, identify terminating and repeating decimals, convert decimals into rational numbers, and perform operations on decimal numbers. Discover the conversion process of repetitive non-terminating decimals into fractions. Simplify the process with examples and clear explanations.

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Decimal Conversions & Operations: Fractions, Terminating & Non-Terminating Decimals

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  1. Decimals

  2. Decimal form can be obtained from Fraction by Division Convert the denominator into 10 or power of 10 and write Equivalent Fraction Mili-Unit– 1/1000 Mili- Kilo – 1/1 Million Centi –Kilo –1/ 1 Lac Unit-Kilo-- 1/1000 Unit-Mili – 1000 Kilo-Mili – 1 Million Kilo-Centi –1 Lac Kilo-Unit--1000

  3. Terminating Decimals Non-Terminating Decimals Non-Terminating Repeating Decimals 1/3,2/7,25/12 Non- Terminating Non-Repetitive Decimal 22/7 , Bring the Fraction into it’s LOWEST FORM To Find for Non- Terminating Decimals- observe prime factors of the denominator. If 2 and 5 are the prime factors of the denominator– The Fraction must be terminating If in addition any other prime number is a factor of Denominator –It’s non terminating (even if it may include 2 or 5 as prime factors ) Eg- 1/16 (T) ; 1/40(T) 1/14 (NT) : 1/70 (NT)

  4. CONVERSION OF TERMINATING DECIMALS INTO RATIONAL NUMBERS 1.2= 1.2X10/10 =12/10=6/5 – Mixed 0.2=0.2X10/10= 2/10 1.23= 1.23X100/100= 123/100-Mixed 0.567 = 0.567X1000/1000= 567/1000 OPERATION OF DECIMAL NUMBERS Addition Subtraction Multiplication Division

  5. Multiplication of Decimals Division of Decimals – Make the Denominator an Integer using Equivalent Fraction

  6. Repetitive Non Terminating Decimals to Fraction

  7. COVERT Take – 0.333333333333 =X 10 X = 3.333333333 9X= 10 X- X = 3.333333 – 0.333333 = 3 X =3/9=1/3

  8. Convert 0.444… into a fraction Let x= 0.444… Since the recurring decimal has a one-digit pattern we multiply this expression by 10 10x= 4.444… x= 0.444… 9x= 0 0 4. 0 ... 4 9 x= 4 9 0.444… =

  9. Convert 0.363636… into a fraction Let x= 0.363636… Since the recurring decimal has a two-digit pattern we multiply this expression by 100 100x= 36.3636… x= 0.3636… 99x= 0 0 0 36. 0 ... 4 11 36 99 = x= 4 11 0.363636… =

  10. Convert 0.411411411… into a fraction Let x= 0.411411411… Since the recurring decimal has a three-digit pattern we multiply this expression by 1000 1000x= 411.411411… x= 0.411411… 999x= 0 0 0 0 411. 0 0 ... 137 333 411 999 = x= 137 333 0.411411411… =

  11. Convert 0.3777… into a fraction Let x= 0.3777… Since the recurring decimal has a one-digit pattern we multiply this expression by 10 10x= 3.777… x= 0.377… 9x= 0 0 3. 4 ... 17 45 34 90 3.4 9 = = x= 17 45 0.3777… =

  12. Convert 1.01454545… into a fraction Let x= 1.01454545… Since the recurring decimal has a two-digit pattern we multiply this expression by 100 100x= 101.454545… x= 1.014545… 99x= 4 0 0 0 100. 4 0 ... 10044 9900 2511 2475 100.44 99 = = x= 279 275 0.01454545… =

  13. 5 11 5 11 It is worth noting a pattern in some recurring decimals: 107 999 4 9 31 99 0.107107… = 0.444… = 0.313131… = 23 999 7 9 8 99 0.023023… = 0.777… = 0.080808… = 163 999 5 9 37 99 3.163163… = 2.555… = 1.373737… = 3 2 1 This might save a bit of work when converting: “write as a decimal” x9 45 99 0.454545… = = x9

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