Gyaanshalaa

Base Conversion 1. Decimal to Other Base System 2. Other Base system to Decimal   Decimal to Other Base System : Step - 1 : Divide the Decimal number (Base 10) to be converted by the values of New Base. Step - 2 : Get the Remainder from the Step 1  and write it aside. Step - 3 : Divide the Quotient of the Step 1 by the New Base again. Step - 4 : Again obtain the Remainder from Step 3 and note it aside. Repeat these steps, and get the Remainders until the Quotient becomes Zero . Step - 5 : Arrange the obtained Remainders in the Reverse Order .  KEY HIGHLIGHTS :  The Remainder that is obtained Last is  MOST SIGNIFICANT DIGIT (M.S.D.) And ,the Remainder that is obtained at the Step 1 is the LEAST SIGNIFICANT DIGIT. (L.S.D.) Example : Convert  34₁₀  into Binary. Sol :  Step  Operation Quotient Remainder Step 1 34 / 2 17 0 Step 2 17 / 2 8 1 Step 3 8 / 2 4 0 Step 4 4 / 2 2 0 Step 5 2 / 2 1 0 Step 6 1 / 2 0 1 On arranging the Remainder...

  Ratio & Proportion Ratio : The representation of same time of quantities in the simplest fraction. Example : Ratio between marks of Girls and marks of Boys.                    Ratio between the Height of 1st and 2nd Person. The simplest fraction x/y is represented as x:y. Here x is called the Antecedent and y is called the Consequent. Different types of Ratios are : Duplicate Ratio : It is the ratio of squares of two numbers.                                                                         Duplicate Ratio of the fraction X/Y is given as : X/Y = X ² / Y ² or...