Students can go through AP 6th Class Maths Notes Chapter 1 Knowing Our Numbers to understand and remember the concepts easily.
Class 6 Maths Chapter 1 Notes Knowing Our Numbers
→ To represent any number, we use ten symbols; namely 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 which are called digits.
→ Numbers help us to compare collection of two or more similar objects and we can decide which collections is bigger or smaller.
→ Comparision of numbers help us to arrange the objects in increasing or decreasing order.
→ Given two numbers, one with more digits is the greater number. If the number of digits in two given numbers is the same, that number is larger, which has a greater leftmost digit. If this digit also happens to be the same, we look at the next digit on the left and so on.
→ Informing 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.
→ The smallest four digit number is 1000 (one thousand). It follows the largest three digit number 999. Similarly, the smallest five digit number is 10,000. It is ten thousand and follows the largest four digit number 9999. Further, the smallest six digit number is 1,00,000. It is one lakh and follows the largest five digit number 99,999. This carries on for higher digit numbers in a similar manner.
→ Use of commas helps in reading and writing large numbers. In the Indian system of numeration we have commas after 3 digits starting from the right and thereafter every 2 digits. The commas after 3rd, 5th and 7th digits to separate thousand, lakh and crore respectively. In the International system of numeration commas are placed after every 3 digits starting from the right. The commas after 3rd and 6th digits to separate thousand and million respectively.
→ Large numbers are needed in many ways in daily life. For example, for counting number of students in a district, number of people in a village or town, money paid or received in large transaction (paying and selling), in measuring large distances say between various cities in a country or in the.world and so on.
→ Remember that kilo means 1000, centi means 100th part and milli means 1000th part. Thus, 1 kilometre = 1000 metres, 1 metre = 100 centimetres or 1000 millimetres etc.
→ There are a num ber of situations in which we do not need the exact quantity but need only a reasonable guess or an estimate. For example, while stating how many spectators watched a particular International hockey match, we state the approximate number, say 51,000, we do not need to state the exact number.
→ Estimation involves approximating a quantity to an accuracy required. Thus, 4,117 may be approximated to 4,100 or to 4,000, i.e., to the nearest hundred or to the nearest thousand depending on our need.
→ In number of situations, we have to estimate the outcome of number operations. This is done by rounding off the numbers involved and getting a quick, rough answer.
→ Use of numbers in Indo-Arabic. system and International system.
→ Estimation and Rounding off numbers : We usually round off the numbers to the
nearest 10’s, 100’s, 1000’s, 10000’s, ………. etc.
Rounding off the numbers to the nearest tens :
81 is nearer to 80 than 90. So 81 will be rounded off to 80.
87 is nearer to 90 than 80. So 87 will be rounded off to 90.
85 is at equal distance from 80 and 90 but by convention it is rounded off to 90.
Rounding off the numbers to nearest hundreds :
220 is nearer to 200 than 300. So 220 is rounded off to 200.
280 is nearer to 300 than 200. So it is rounded off to 300.
250 is at equal distance from 200 and 300 but by convention it is rounded off to 300.
→ Introduction of large numbers.
Write the smallest and greatest of all two digit, three digit, four digit, five digit, six digit, seven digit, eight digit numbers.
Solution:
The smallest two digit number is 10.
The greatest two digit number is 99.
The smallest three digit number is 100.
The greatest three digit number is 999.
The smallest four digit number is 1000.
The greatest four digit number is 9999.
The smallest five digit number is 10000.
The greatest five digit number is 99999.
The smallest six digit number is 100000.
The greatest digit number is 999999.
The smallest seven digit number is 1000000.
The greatest seven digit number is 9999999.
The smallest eight digit number is 10000000.
The greatest eight digit number is 99999999.
Place value of large numbers: Use of ‘comma’ helps us in reading and writing of large numbers.
Ex. 25,240; 1,30,407; 45,04,155; 1,22,00,320.
1 crore = 100 lakhs
= 10,000 thousands
1 lakh = 100 thousands
= 1000 hundreds
→ International system of Numeration: In the international system of numeration, we use ones, tens, hundreds, thousands and then millions. One million is athousand thousands or ten lakhs. Commas are used to mark thousands and millions. It comes after every three digits from the right. Suppose the number is 45690255.
| Indian system of numeration | International system of numeration |
| 4,56,90,255
Four crore fifty six lakhs ninety thousand two hundred fifty five. |
45,690,255
Forty five million six hundred ninety thousand two hundred fifty five. |
Comparison of places in both the systems for better understanding.
From the above table, the relations between these systems can be understood as follows :
10 lakhs = 1 million
1 crore = 10 million
10 crore = 100 million
100 crore = 1 billion
→ Large numbers used in daily life situations:
The unit of length is meter.
The unit of weight is kilogram.
The unit of volume is litre.
The unit of time is second.
We use centimeter of measuring the length of a pencil. We use meter for measuring the length of a saree. We use kilometer for measuring the distance between two places. We use millimeter for measuring the thickness of paper.
10 millimeters = 1 centimeter
100 centimeters = 1 meter
= 1 kilometer = 1000 × 100 × 10 millimeters
= 10,00,000 m.m
1 kilogram = 1000 gms and 1 gram = 1000 milligrams
1 kilolitre = 1000 litres
→ Ascending Order (A.O) : Ascending order means arrangement from the smallest to the greastest.
→ Descending Order (D.O) : Descending order means arrangement from the greatest to the smallest.