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Decimals. 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
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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
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)
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
Multiplication of Decimals Division of Decimals – Make the Denominator an Integer using Equivalent Fraction
Repetitive Non Terminating Decimals to Fraction
COVERT Take – 0.333333333333 =X 10 X = 3.333333333 9X= 10 X- X = 3.333333 – 0.333333 = 3 X =3/9=1/3
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… =
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… =
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… =
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… =
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… =
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