Chapter 1 Knowing Our Numbers Class 6 Quick revision Notes Maths

Numbers

• Symbols used for counting and measuring the objects are called numbers.

• A group of digits, denoting a number, is called a numeral.

• Writing a number in words is called numeration.

• 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits or figures.

• Counting Numbers are called natural numbers.

• Counting Numbers alongwith zero is called whole numbers.

• Successor: The number that comes just after a given number. Example: Successor of 7 = 7+1=8

• Predecessor: The number that comes just before a given number. Example: Predecessor of 7 = 7 -1 = 6

Comparing Numbers

• The number with more digits > number with less digits. For example, 215 > 81.

• If two numbers have the same number of digits, then compare the digits on the extreme left and decide. If the extreme left digits are the same, compare the next digits to the right, and so on… For example: 57405926> 57405921.

• Ascending order means arrangement from the smallest to the greatest.

• Descending order means arrangement from the greatest to the smallest.

• The smallest four digit number is 1000 (one thousand). It follows the largest three digit number 999. 

• The smallest five digit number is 10,000. It is ten thousand and follows the largest four digit number 9999.

• The smallest six digit number is 100,000. It is one lakh and follows the largest five digit number 99,999. This carries on for higher digit numbers in a similar manner.

Indian System of Numeration

• We use ones, tens, hundreds, thousands, lakhs and crores.

• Commas are used to mark thousands, lakhs, and crores. For example: 3, 32, 40, 781 – Three crore thirty two lakh forty thousand seven hundred eighty one.

• Face value of a digit : The face value of a digit remains as it is, whatever place it may be occupying in the place value chart.

• Place value of a digit : The place value of digit in a numeral depends upon the place it occupies in the place value chart.

• Place value of a digit in a number = Face value × Position value.

International System of Numeration

• We use ones, tens, hundreds, thousands and millions. To express numbers larger than a million, a billion is used. 1 billion = 1,000 million.

• Commas are used to mark thousands and millions. For example: 3, 32, 40, 781 – Thirty three million two hundred forty thousand seven hundred eighty-one.

Large Numbers in Practice

Length

• 1 kilometre = 1000 metre

• 1 metre = 10 decimetre = 100 centimetre = 1000 millimetre

Mass

• 1 kilogram = 1000 grams

• 1 gram = 10 decigram = 100 centigram = 1000 milligram.

Capacity

• 1 litre = 10 decilitre = 100 centilitre = 1000 millilitre

Estimation (Rounding Off)

Nearest 10

• If the digit in the units place is less than 5, then the units digit is replaced by 0.

• If the digit in units place is greater or equal to 5, then the unit place is replaced by zero and tens place is increased by 1.

Nearest 100

• If the digit in the tens place < 5, then the tens and units place are replaced by zero.

• If the digit in the tens place is equal to or > 5 then the tens and units place is replaced by zero and the hundreds place is increased by 1.

Nearest 1000

• If the digit in the hundreds place is < 5, then the hundreds, tens and units place is replaced by 0.

• If the digit in the hundreds place is equal to or > 5, then the hundreds, tens and units place is replaced by 0 and the thousands place is increased by 1.

Roman Numerals

• Roman numerals are one of the early systems of writing numerals.

I = 1

II = 2

III = 3

IV= 4

V = 5

X = 10

L = 50

C = 100

D = 500

M = 1000

Rules of Roman Numeral System

• If a symbol is repeated, its value is added as many times as it occurs.

• A symbol is not repeated more than three times. But the symbols V, L and D are never repeated.

• If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.

• If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.

• The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted. The symbol I can be subtracted from V and X only. The symbol X can be subtracted from L, M and C only.