When someone gets you a surprise gift you are likely to estimate its approximate cost. Thus, in English estimation is the rough calculation of the value or the extent of something. Similarly, an approximation is a value that is nearly correct but not exact.
In mathematics, you will come across many situations where in you need to estimate.
Estimation means to make a judgment of quantities, approximate calculation of size, cost, population etc.
Approximation means almost correct amount. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix, ap- meaning to.
In this chapter, you will learn about estimation and approximation.
The procedure of estimation depends upon the following:
Fractional numbers whose denominators ar 10 , 100, 1000 etc, are called decimal fractions or decimals. The dot “ . “ is called the decimal point. For Example : (i) 3 10 is expressed as 0.3 (ii) 1 100 is expressed as 0.01 II. Conversion of Decimals Example : convert the following fraction into decimals (i)
Solutions : 8÷3 = 0.375
= 5.375
III . Conversion of Units : 1 kilometre = 1000 metres 1 metre = 100 centimetres 1 centimetre = 10 milimetres 1 decimetre = 10 centimetre 1 metre = 10 decimetres 1 hectomere = 10 decametres 1 Kilometre = 10 hectometres
III . Conversion of Mass : 1 kilometre = 1000 grams 1 grams = 100 centigrams 1 centigram = 10 miligrams 1 decigram = 10 centigrams 1 gram = 10 decigram 1 hectogram = 10decagrams 1 Kilogram = 10hectograms
A fraction means a part of a whole (group or region). Every fraction has a numerator and a denominator. In the fraction 3/5 , 3 is the numerator part and 5 is the denominator part.
Types of Fraction:- (i) Proper Fraction: Fraction in which the numerator is less than the denominator, is called proper fraction. For eg: 4/5 , 6/11, 999/1000. (ii) Improper Fraction: Fraction in which the numerator is either equal to or greater than the denominator, is called the improper fraction. For eg: 3/5 , 6/5, 1000/999. (iii) Like Fraction: Fraction having the same denominator are called like fractions. For eg: 3/5, 5/5, 6/5 (iv) Unlike Faction: Fraction having different denominators are called unlike fractions. For eg: 3/5, 4/3, 4/7 (v) Mixed Fraction : Mixed Fraction like 1 4 1 (vi) Equivalent Fraction:Two or more factions having the same value or representing the same part of whole are called equivalent fraction. Example. Write an equivalent fraction of 4/5 with numerator as 12. Solution:- 1 st Method : To get 12 as the numerator, we have to multiply 4 by 3. Therefore, denominator 5 should also be multiplied by 3.
So, 4/5 = 4 x 3 5 x 3 = 12/15 2 nd Method : 4 12 5 ? = 4 x ? = 12 x 5 12 x 5 4 = 15 So, 4/5 = 12/15 Hence, 12 / 15 is an equivalent fraction of 4/5 Example : Meera cuts 54 m of cloth into some pieces, each of length 3 3/8 meters. How many pieces does she get. Solution : Total length of clothe = 54m Length of each piece = 3 3/8 m = 27/8 m No. of pieces formed = 54 / 27/8 = 54 x 8 /27 = 16 Hence , 16 pieces each of length 3 3/8 m can be cut down from the cloth of 54 m length.
Conceptual division:- • Introduction of Set : A set is a collection or group of objects/elements which have a similar characters.
• Way of Representing Set a. Elements of a Set b. Properties of Set
• Representation of Set a. Listing Method (Roster form) b. Rule Method ( Set-builder form)
• Types of Set a. Equal Sets b. Empty Set or Null Set or Void Set c. Non-Empty Set or Overlapping Set d. Singleton Set e. Finite Set f. Infinite Set g. Null or Empty or Void Set h. Equivalent Set i. Disjoint Set j. Cardinality of Set
• Examples : • Disjoint Set
Q.1Two sets are given by A = x , y, z and B = 1,2,3,4,5
Solution : Clearly , sets A and B have no element common to both . Therefore sets A and B are disjoint sets.
Q.2 Find the cardinality of the set A = 2 , 4,8,10,12
Solution : Since , set A = 2, 4, 8, 10, 12 has total 5 elements. Hence , the cardinality of the set A is 5.
Unit 3 Utility Service of Banking Notes| Class 9th Banking & Insurance Video
Detailed Explanation of Unit 3: Utility Services of Banking
1. Credit Cards & Debit Cards
Modern banking provides two essential payment instruments: credit cards and debit cards, each catering to different financial needs.
A. Credit Cards
A credit card allows the user to borrow funds up to a pre-approved limit to pay for goods and services.
Features:
Buy now, pay later: Allows deferred payment.
Interest-free period: Typically 30–50 days if the bill is cleared on time.
Reward programs: Cashback, discounts, or reward points on purchases.
Real-Life Example:
An individual uses a credit card to book flight tickets online, earning reward points redeemable for discounts on future purchases.
B. Debit Cards
A debit card deducts money directly from the user’s bank account for transactions.
Features:
Direct payment from savings/current account.
No interest or borrowing involved.
Suitable for people managing expenses within their account balance.
Real-Life Example:
A customer pays for groceries using their debit card, with the amount deducted immediately from their savings account.
C. Differences Between Credit and Debit Cards
Feature
Credit Card
Debit Card
Payment Mode
Borrowed funds
Own account balance
Interest
Charged on overdue payments
No interest
Eligibility
Requires a good credit score
Available to most account holders
Use in Emergencies
Suitable for large purchases
Limited by account balance
Solution Example:
Q1. Differentiate between credit and debit cards with examples. Ans:
A credit card allows borrowing funds, while a debit card deducts money from the user’s account.
Example: Booking tickets with a credit card involves borrowed money, while paying bills with a debit card uses personal funds.
2. Automated Teller Machines (ATMs)
ATMs are self-service banking terminals enabling customers to perform various financial transactions.
A. Functions & Uses of ATMs
Cash withdrawal: Convenient access to funds anytime.
Balance inquiry: View account balances instantly.
Fund transfer: Transfer money between accounts.
Bill payments: Pay utility bills directly via ATMs.
Real-Life Example:
A traveler withdraws cash from an ATM during a holiday in a remote town.
B. Customer Complaints Management for ATM Transactions
Common Issues:
Cash not dispensed but debited.
Card stuck or malfunctioning.
Resolution Process:
Register complaints via helpline, online portals, or branch visits.
Resolution typically occurs within 7 working days.
C. Evolution of ATMs
First ATM: Introduced in the late 1960s.
Technological Advancements: From simple cash dispensing to complex transactions like deposits and fund transfers.
D. Structure of ATMs
Input Devices: Keypad and card reader.
Output Devices: Display screen, receipt printer, and cash dispenser.
Software: Ensures secure and seamless transactions.
Solution Example:
Q2. What are the functions of ATMs, and how do they resolve customer complaints? Ans: Functions: Cash withdrawal, balance inquiry, fund transfer, and bill payments. Complaint Resolution: Customers can report issues through helplines or branches, with most problems resolved within 7 days.
3. Core Banking
Core banking refers to centralized systems enabling customers to access their accounts and services from any branch or digital platform.
Features of Core Banking:
Anywhere Banking: Access accounts from any branch or ATM.
Digital Services: Internet and mobile banking integration.
Real-Life Example:
A customer deposits a cheque at a branch in Mumbai, and the amount is accessible in their Delhi branch account instantly.
Solution Example:
Q3. What are the features of core banking? Ans: Core banking allows real-time processing, anywhere banking, and digital services integration, ensuring customer convenience.
4. Standing Instructions
Standing instructions are predefined orders given by customers to banks to execute recurring payments like utility bills or loan EMIs.
a. Specimen of Standing Order:
Date: [DD/MM/YYYY] To: [Bank Name] Subject: Standing Instruction for Monthly Payment Instruction: Debit ₹5,000 monthly from my account for electricity bill payment.
Solution Example:
Q4. Define standing instructions with an example. Ans: Standing instructions automate recurring payments. Example: Setting up an order to pay monthly rent via account debit.
Summary
Utility services such as credit/debit cards, ATMs, core banking, and standing instructions have transformed banking, enhancing convenience and efficiency for customers. These tools cater to diverse financial needs and simplify banking experiences.
10 Most Important Questions with Detailed Solutions
Differentiate between credit and debit cards. Ans: Credit cards use borrowed funds, while debit cards deduct from the user’s account balance.
List the uses of ATMs. Ans: Cash withdrawal, balance inquiry, fund transfer, and bill payments.
Explain the role of core banking in modern banking services. Ans: Core banking enables anywhere banking, real-time processing, and digital service integration.
What are standing instructions? Provide an example. Ans: Standing instructions automate recurring payments. Example: Loan EMI payments.
State the features of credit cards. Ans: Deferred payment, interest-free periods, and reward programs.
What is the process for resolving ATM complaints? Ans: Complaints can be filed via helplines, online portals, or bank branches, resolved within 7 days.
What is the evolution of ATMs? Ans: Initially introduced for cash dispensing, ATMs now support deposits, fund transfers, and more.
What are the advantages of core banking for customers? Ans: Ensures flexibility, instant transaction updates, and digital convenience.
Describe the structure of ATMs. Ans: Includes input devices (keypad, card reader), output devices (screen, printer, dispenser), and secure software.
Explain how ATMs support real-life scenarios. Ans: ATMs provide 24/7 access to cash and services, ensuring convenience during emergencies.
In this system, we use ten symbols namely: 0, 1, 2,3,4,5,6,7,8 and 9 to represent any number. These symbols are called digits.
Concept 2: Place value and Face value
Place value of a digit in a number depends on the place it occupies in the number
The face value of a digit is the digit itself
‘0’ is the only digit whose face value and place value both are same, i.e. the face value of 0 is 0 and place value of 0is also 0.
Example 1. Find the place value of all the digits in the number 35268 Soln. In the number 35268, we have • The place value of 8 = 8 x 1 = 8 • The place value of 6 = 6 x 10 = 60 • The place value of 2 = 2 x 100 = 200 • The place value of 5 = 5 x 1000 = 5000 • The place value of 3 = 3 x 10000 = 30000
Expanded form of a number: A number is expanded on the basis if the place values of the digits. For instance, Number = unit’s place x (unit) + ten’s place x (10) + hundredth place x (100) + thousand’s place x (1000) + … and so on. Comparison of 2 numbers: To decide which one is bigger, remember the following: 1) Of the 2 numbers the number having more digits is bigger 2) If 2 numbers have an equal number of digits, then the number having the larger digit in the leftmost place is bigger. If the digit in the leftmost place are equal then the number having the larger digit in the place on the right of the equal digits is bigger, and so on
Example 2. Compare the numbers:
8325 and 14103
60714 and 52130 Soln. 1) The first number has four digits while the second has five digits. So, the second number is bigger. 2) The 2 numbers have an equal number of digits, however, 6<5. So, 60714 is the biggest number.
Concept 3: Natural number and Whole number
Natural number and Whole number
Natural number: The counting number 1, 2,3,4,5,6, …, are called natural numbers. 1 is the first and the smallest natural number. Any natural number can be obtained by adding 1 to its previous natural number. There is no last or largest natural number. Therefore, there are infinite whole numbers.
Whole number: The number ‘0’ altogether with natural number, called whole numbers, i.e. 0,1,2,3,4,5, … etc. are called whole numbers 0 is the first and the smallest whole number There is no last or largest whole number. Therefore, there are infinite whole numbers. Examples:
Find the face values of all the digits in the number 83245. Soln. In the number 83245 • The face value of 5 is 5. • The face value of 4 is 4. • The face value of 2 is 2. • The face value of 3 is 3. • The face value of 8 is 8.
Find all the possible three digit numbers using the digits 1,3,5 taking each diggings Keeping 1 at the ones place the numbers formed are 751 and 571 Keeping 5 at the ones place, the numbers formed are 157 and 517 So, the required numbers are 751, 571, 175, 715, and 157,517.
