Decimals Decimal form can be obtained from Fraction

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 Kilo-Centi – 1 Lac Kilo-Unit--1000

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. 2 X 10/10 =12/10=6/5 – Mixed 0. 2=0. 2 X 10/10= 2/10 1. 23= 1. 23 X 100/100= 123/100 -Mixed 0. 567 = 0. 567 X 1000/1000= 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. 333333 =X 10 X = 3. 33333 9 X= 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 10 x = 4. 444… x = 0. 444… 9 x = 4. 000. . . x= 4 9 4 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 x = 36. 3636… x= 0. 3636… 99 x = 36. 0000. . . 36 = 4 x= 99 11 4 0. 363636… = 11

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 x = 411411… x= 0. 411411… 999 x = 411. 000000. . . 411 = 137 x= 999 333 137 0. 411411411… = 333

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 10 x = 3. 777… x = 0. 377… 9 x = 3. 400. . . 3. 4 = 34 = 17 x= 90 45 9 17 0. 3777… = 45

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 x = 101. 454545… x= 1. 014545… 99 x = 100. 440000. . . 100. 44 = 10044 = 2511 x= 9900 2475 99 0. 01454545… = 279 275

It is worth noting a pattern in some recurring decimals: 4 0. 444… = 9 31 0. 313131… = 99 107 0. 107107… = 999 7 0. 777… = 9 8 0. 080808… = 99 23 0. 023023… = 999 37 1. 373737… = 1 99 3. 163163… = 3 2. 555… = 2 5 9 This might save a bit of work when converting: “write x 9 5 as 11 a decimal” 45 5 = = 11 x 9 99 0. 454545… 163 999