Higher Algebra Hall & Knight Scales of Notation (Chapter 7) Solutions

Hall and Knight Higher Algebra Solutions for Chapter 7 ‘Scales of Notation’ is a perfect guide for competitive exams preparation along with Class 12. Our solutions comprise of all the essential topics which help in forming a stronger command of the fundamentals of notation along with the systems of notation, integral number on a proposed scale and expression of a radix fraction. This chapter of Higher Algebra by Hall and Knight covers vital concepts regarding the difference between a number and the sum of its digits divisible by (r – 1) and proof of rule for ‘casting out the nines’.  The chapter also includes detailed theoretical explanations along with solved examples to help you form a better understanding of the chapter. You will also learn about the concepts of the denary scale of notation, radix, fractional representation, radix – fractions, radix – points and divisibility from the chapter. 

Higher Algebra By H.S. Hall and S.R. Knight Scales of Notation solutions include 2 exercises with 56 questions. These exercise questions would help you in getting you familiar with all the possible kinds of questions which can be formed from the chapter in competitive exams like IIT JEE and NEET. Once you solve these questions, you will learn to solve problems which deal with scale, radix, multiplicand, radix fractions, recurring decimals and duodenary scales. 

Hall & Knight Algebra Mathematics book with solutions by Instasolv for Scales of Notation has been prepared to make sure that your time is invested in enhancing your concepts and preparation rather than in reaching out to various resources. You will find all the exercise-wise solutions for the chapter here arranged in a systematic order. All our solutions are checked at various levels by our experts to ensure that they are 100% accurate and up to date. 

Important Topics for Hall and Knight Higher Algebra Solutions Chapter 7: Scales of Notation

Scales of Notation

In this chapter, you will learn about the scales of notation. When an ordinary number with which you are acquainted in arithmetic is expressed by the means of multiples which are to the powers of 10 the method of representation is termed as the common or denary scale of notation. For example, consider the following representation 

25 = 2 X 10 + 5 

Here this representation is done in such a way that the arithmetic value has been expressed in its multiples of power 10 i.e. 2 X 10 + 5. The ten here is known as the radix of the scale. The nine digits and the zero are symbols that are employed in this system of notation.

Types of Scales 

In this chapter, you will encounter different kinds of scales. You will learn about the basic types – the binary scale, the tertiary scale, the quaternary scale, the senary scale, the nonary scale and the denary and non-denary scale. You will also come across the undenary scale and the duodenary scale. There are different kinds of symbols which are required to represent the digits that are greater than 9. 

You learn to work with these scales in order to perform different operations like addition, subtraction, multiplication and division on the series of numbers and different digits which you will encounter in the chapter. From the ordinary arithmetic operations to the condition based problems, these scales form a major portion of the chapter and the exercise questions. 

Exercise Discussions of Hall and Knight Higher Algebra Solutions Chapter 7: Scales of Notation

Example VII a 

  • There are a total of 16 questions in the first exercise of Scales of Notation by Hall & Knight. 
  • The exercise begins with simple questions where you are required to add the given numbers (comprised of more than three digits) and the addition has to be performed in the scale of five.
  • There is another question where you are required to perform subtraction under similar conditions as the previous question 
  • There are questions where you get to deal with duodenary and nonary numbers and scales. 
  • Then there are questions where you are required to perform multiplication and division and at some instances, you are also required to find the square roots.
  • The exercise also contains questions which include the idea of lowest common factor and Greatest common factor. 

Example VII b 


  • There are a total of 40 questions in this exercise. 


  • The first five questions of this exercise contain three to six-digit numbers which are supposed to be expressed in the scales of different numbers like nine, five, seven, three and nine
  • Then there are certain questions where you are required to transform numbers from the scale of one digit to another.
  • The exercise also has questions where you are required to express septenary numbers in powers.
  • There are problems regarding denary vulgar fractions in their lowest terms, denary fractions and septenary fractions.
  • The last section of the exercise contains word problems which deal with a radix, ordinary scales, perfect squares, equidistant digits, odd radix and consecutive integers.  



Why Use Solutions for Higher Algebra by Hall and Knight Chapter 7: Scales of Notation by Instasolv?

  • Instasolv provides chapter-wise solutions for Elementary Algebra and Higher Algebra by Hall & Knight books that will help you in preparing for JEE and NEET like competitive tests. 


  • We have ensured that no corner of the chapter is left untouched and every question is carefully dealt with in our solutions. 


  • For Scales of Notation Solutions of Higher Algebra by Hall & Knight, we have given special emphasis on ensuring that all our answers are provided according to the current syllabus and curriculum for Class 12 along with JEE and NEET. 
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