KNOWING OUR NUMBERS
Natural Numbers
Counting numbers 1, 2, 3, 4, ...... etc. are called Natural numbers. The smallest natural number is 1 and there is no
largest natural number.
Digits and Place value
Numbers are formed using the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. These symbols are called digits or figures.
To find the place value of a digit in a number, multiply the digit with the value of the place it occupies.
1. Indian place value chart for 9-digitnumber.
2. International place value chart for a 9 digitnumber.
3. Inserting commas: Inserting commas helps in reading and writing large numbers. A comma isinserted after
each period in both thesystems.
Comparing numbers
i. When numbers of digits are different, then the number having more number of digits isgreater.
ii. When numbers of digits are the same, compare the leftmost digits in the two numbers. The number with the greater
leftmost digit is greater. In case the leftmost digits are the same, then compare the next left digits in both the numbers.
The number with greater digit is greater. Continue this process, until you come across unequal digits at the corresponding
places.Then compare those two digits to find the greater number.
4. Place value of a digit in a number is the digit multiplied by itsplace.
5. Face value of a digit remains the same, whatever place it may be occupying in the place valuechart. In other words,
face value is the actual value of thedigit.
6. Numbers can be arranged in ascending or descending order. Ascending order meansarrangement from smallest to the greatest.
Descending order means arrangement from largest tosmallest.
7. The number which is one more than the given number is called itssuccessor.
8. The number which is one less than the given number is called itspredecessor.
9. There are certain situations where we have to give an idea about a number without actual calculation. This is calledestimation.
10. Rounding a number to nearestten
i. See the ones digit of the givennumber.
ii. If ones digit is less than 5, replace ones digit by 0, and keep the other digits as theyare.
iii. If ones digit is 5 or more, increase tens digit by 1, and replace ones digit by0.
Some important terms
• The arrangements of numbers from the smallest to the greatest is called ascending order.
• The arrangement of numbers from the greatest to the smallest is called descending order.
Place Value of digit
Let’s discuss the place value of digits in the number and how a number can be written in that form
Indian system of numeration
Values of the places in the Indian system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousand, Lakhs,
Ten Lakhs, Crores and so on.
The following place value chart can be used to identify the digit in any place in the Indian system.
We can use below table format for easily reading and writing the Number
Use of Commas
Commas added to numbers help us read and write large numbers easily. As per Indian Numeration, Commas are used
to mark thousands, lakhs and crores. The first comma comes after hundreds place (three digits from the right) and marks
thousands. The second comma comes two digits later (five digits from the right). It comes after ten thousand place and marks
lakh. The third comma comes after another two-digits (seven digits from the right). It comes after ten lakh place and marks crore
International system of numeration
Values of the places in the International system of numeration are Ones, Tens, Hundreds, Thousands, Ten thousands,
Hundred thousands, Millions, Ten millions and so on.
1 million = 1000 thousands,
1 billion = 1000 millions
Following place value chart can be used to identify the digit in any place in the International system
Estimation of the Numbers
A reasonable guess of the actual value is called an estimate.
A quick, rough estimate of the result of number operations can be done by rounding off the numbers is involved.
Rules of Estimation
• Estimating numbers to the nearest tens is done by rounding off numbers 1, 2, 3 and 4 to 0 and number 6, 7, 8, 9 to 10.
• Estimating numbers to the nearest hundreds is done by rounding off numbers 1 to 49 to 0 and numbers 51 to 99 to 100.
• Estimating numbers to the nearest thousands is done by rounding off numbers 1 to 499 to 0 and the numbers 501 to 999 to 1000.
Estimation involves approximating a quantity to an accuracy required. We can apply the above rules depending on the accuracy required.
We can estimate Sum, difference and Multiplication by applying the rules of estimation also. We can apply the above rules depending
on the accuracy required and how quickly answer can be find out
Roman Numerals
Roman Numerals system is another system used apart of Hindu-Arabic system.
The Roman numerals are
Rules of the system
• In Roman numerals a symbol is not repeated more than three times, but the symbols V, L and D are never repeated.
• Roman numerals are read from left to right and the letters of Roman numerals are arranged from the largest to the smallest.
• If a symbol of smaller value is written to the right of a symbol of greater value, then its value gets added to the value of greater symbol.
VI = 5 + 1 = 6
• If a symbol of smaller value is written to the left of a symbol of greater value, its then value is subtracted from the value of the greater symbol.
IV = 5 – 1 = 4
• The symbol I can be subtracted from V and X only.
The symbol X can be subtracted from L, M and C only.
Importance of Brackets
Brackets help in simplifying an expansion with more than one mathematical operation.
In an expression that includes brackets, the numbers inside the brackets must be simplified into a single.
11. Rounding a number to nearesthundred
i. See the tens digit of the givennumber.
ii. Iftensdigitislessthan5,replaceeachoftensandonesdigitby0,andkeeptheotherdigitsas theyare.
iii. If tens digit is 5 or more, increase hundreds digit by 1, and replace each digit on its right by0.
12. Rounding a number to nearestthousand
i. See the hundreds digit of the givennumber.
ii. Ifhundredsdigitislessthan5,replaceeach ofhundreds,tensandonesdigitby0,andkeepthe other digits as theyare.
iii. If hundreds digit is 5 or more, increase thousands digit by 1, and replace each digit on its rightby 0.
13. Estimating sum ordifference
i. Select the smallernumber.
ii. Round off the given numbers to the highest place value of that of the smallernumber.
iii. Add or subtract the rounded numbers as per thequestion.
14. Estimatingproduct
i. Round off each factor to its nearest greatestvalue.
ii. Multiply the rounded offfactors.
15. Estimatingquotient
i. Round off the dividend to the nearest multiple of the divisor so that division becomeseasy.
ii. Divide to get thequotient.
16. Roman numeral system is one of the systems in which certain symbols are used torepresent numbers.
There are seven symbols to represent numbers of Hindu-Arabic system in Roman numeration.
17. While writing numbers in Roman system, certain rules are to be followed. Theyare:
i. Repetition of a symbol in Roman numeral meansaddition.
ii. A symbol is not repeated more than three times. But the symbols V, L and D are neverrepeated.
iii. Ifanumeraloflesservalueiswrittentotheleft ofagreatervalue,theresultingvalueisobtained by finding theirdifference.
iv. If a numeral of lesser value is written to the right of a greater value, the resulting value is obtained by finding theirsum.
v. The symbols V, L and D are never written to the left of the symbol of greater value. In other words, V, L and D are neversubtracted.
The symbol I can be subtracted from V and X only. The symbol X can be subtracted from L, M and C only.
18. For simplifying a given expression containing brackets, we strictly perform simplification in the following order(VBODMAS):
i. Vinculum
ii. Brackets
iii. of
iv. Division
v. Multiplication
vi. Addition
vii. Subtraction
