What Have We Discussed ?
1.Given two numbers, the one with more digits is the
2.In forming numbers from given digits, we should be careful to see if the conditions under which the numbers are to be formed are satisfied. Thus, to form the greatest four digit number from 7, 8, 3, 5 without repeating a single digit, we need to use all four digits, the greatest number can have only 8 as the leftmost digit.
3.The smallest four digit number is
4.Use of
5.In the Indian system of numeration, we have commas after 3 digits starting from the right and thereafter every 2 digits. The commas after 3, 5 and 7 digits separate thousand, lakh and crore respectively.
6.In the International system of numeration, commas are placed after every 3 digits starting from the right. The commas after 3 and 6 digits separate
7.Large numbers are needed in many places in daily life. For example, for counting number of students in a school, number of people in a village or town, money paid or received in large transactions (paying and selling), in measuring large distances say between various cities in a country or in the world and so on.
8.Remember kilo shows 1000 times larger, Centi shows 100 times smaller and milli shows 1000 times smaller. Thus, 1 kilometre =
Indian place value chart
| Crores | Lakhs | Thousands | Ones | |||||
|---|---|---|---|---|---|---|---|---|
| Ten Crore | Crore | Ten Lakh | Lakh | Ten Thousand | Thousand | Hundred | Tens | Ones |
| 10,00,00,000 | 1,00,00,000 | 10,00,000 | 1,00,000 | 10,000 | 1,000 | 100 | 10 | 1 |
International place value chart
| Millions | Thousands | Ones | ||||||
|---|---|---|---|---|---|---|---|---|
| Hundred Million | Ten Million | Million | Hundred Thousand | Ten Thousand | Thousand | Hundred | Tens | Ones |
| 100,000,000 | 10,000,000 | 1,000,000 | 100,000 | 10,000 | 1,000 | 100 | 10 | 1 |
Units conversion table
| Mnemonic | Prefix | Relation with basic unit | Short Form | Scale |
|---|---|---|---|---|
| King | Kilo | 1 Kilo=1000 units | km=kilometer kL=kiloliter kg=kilogram | 10x10x10 LARGER than a unit |
| Henry | Hecto | 1 hecto=100 units | hm=hectometer hL=hectoliter hg=hectogram | 10x10x LARGER than a unit |
| Died | Deca | 1 deca=10 units | dam=decameter daL=decaliter dag=decagram | 10x LARGER than a unit |
| By | Basic Unit | 1 unit | m=meter L=liter g=gram | Meter (length) Liter (liquid volume) Gram (mass/weight) |
| Drinking | Deci | 10 deci = 1 unit | dm=decimeter dL=deciliter dg=decigram | 10x SMALLER than a unit |
| Chocolate | Centi | 100 centi = 1 unit | cm=centimeter cL=centiliter cg=centigram | 10x10x SMALLER than a unit |
| Milk | Milli | 1000 milli = 1 unit | mm=millimeter mL=milliliter mg=milligram | 10x10x10x SMALLER than a unit |
Section A
Round the number 23,487 to the nearest ten, hundred, and thousand
Answer:
Nearest ten: 23,490
Nearest hundred: 23,500
Nearest thousand: 23,000
Section B
Write the number names for
(a)765,490,786
(b)24,58,765
(a)Answer: Seven hundred sixty five million four hundred ninety thousand sevend hundred and eighty six
(b)Answer: Twenty four lakh fifty eight thousand seven hundred sixty five
Section C
A store sold 785 bags in January, 956 bags in February, and 1,234 bags in March. What is the total number of bags sold in these three months?
Answer: 4,800 - 2,650 =
Section D
Write a number between 5,000 and 6,000 that is divisible by 5 and explain how you know it is divisible by 5
Answer: 5,005; A number is divisible by 5 if it ends in 0 or 5.
Problem 1
Situation: A sports stadium has a seating capacity of 25,000. During a major event, 19,876 people attended.
Questions:
(1)How many seats were left vacant during the event?
(2)Why is it important to have events that bring people together in large numbers?
Answers
(1) Calculating the number of vacant seats:
Vacant seats = 25,000−19,876=5,124 seats
(2) Importance of events that bring people together:
Community Building: Such events foster a sense of community and belonging.
Cultural Exchange: They allow for the exchange of ideas and cultures.
Entertainment and Leisure: They provide a source of entertainment and relaxation.
Economic Benefits: Large events can boost local economies through tourism and related activities.
Problem 2
Situation: Two factories produced 15,876 and 18,542 units of goods respectively in a month.
Questions:
(1)By how many units did the second factory produce more than the first?
(2)Discuss the importance of fair competition between businesses.
Answers
(1) Calculating the difference in production:
Difference in production=18,542−15,876=2,666 units
(2)Importance of fair competition:
Innovation and Improvement: Fair competition encourages businesses to innovate and improve their products and services.
Consumer Benefits: It leads to better quality and more choices for consumers.
Economic Growth: Healthy competition can drive economic growth and job creation.
Ethical Standards: Fair competition promotes ethical business practices and prevents monopolies.
Problem 3
Estimation and Rounding Off
Situation: A school library plans to buy new books. The total cost of 48 science books is ₹19,472. Estimate the cost of each book by rounding off the total cost to the nearest thousand.
Questions:
1. What is the estimated total cost and estimated cost per book?
2. Why is it important to budget and plan for expenses?
Answers
- Estimating the total cost and cost per book:
Estimated total cost = ₹20,000
Estimated cost per book = ₹20,00048 ≈₹417 per book
Estimated cost per book=48₹20,000≈₹417 per book
- Importance of budgeting and planning for expenses:
Financial Management: It helps in managing finances and avoiding overspending.
Resource Allocation: Ensures that resources are allocated efficiently.
Achieving Goals: Helps in setting and achieving financial goals.
Preparedness: Prepares individuals and organizations for unforeseen expenses.
question1
1.Write the smallest and the greatest 5-digit numbers using the digits 0,2,4,6,8 (Repetition of digits is not allowed).
Solution
Given digits are 0, 2, 4, 6, 8
5 – digit greatest number = 86420;
5 – digit smallest number = 20468.
question2
2. Write the following numbers in ascending order. How many of them are even numbers? 63,854, 63,584, 65,348, 68,543, 64,835
Solution
The given numbers are 63,854, 63,584, 65,348, 68,543 and 64,835.
question3
3.What is the successor of greatest 6-digit number?
Solution
Greatest 6-digit number =
Successor of it = 999999 + 1 =
i. e., smallest 7-digit number.
Hence, the required successor = 10,00,000.