Important Formulas: Knowing Our Numbers | Mathematics for Grade 6 PDF Download

(1) Counting numbers 1, 2, 3, 4, 5, 6, ... etc. are known as natural numbers.
(2) 1 is the smallest natural number.
(3) 0. 1. 2, 3, 4, 5, 6, 7, 8, and 9 are called digits, and a group of digits denoting a number is called a numeral or a number.
(4) The method of representing a number in digits or figures is called notation and the method of expressing a number in words is called numeration. There are two methods of numeration:

• The Indian system of numeration
• The international system of numeration.

(1) Place value of a digit in a number = Its face value × Position value
(2) 1 million = 10 lakhs
10 million = 1 crore
100 million = 10 crores
1 billion = 100 crores or 1 Arab.
(3) 1 km = 1000 meter (m)
1 meter = 100 centimetre (cm)
1 cm = 10 millimetre (mm)
1 kilogram (kg) = 1000 grams (gm)
1 litre = 1000 millilitres (m1)

(4) In order to estimate or round off a number to the nearest —
(a) tens:

• replace the one digit by 0 and keep the other digits as they are, if the digit at one place is less than 5.
• increase tens digit by 1 and replace the ones digit by 0, if the digit at ones place is greater than or equal to 5.

(b) hundreds:

• replace each one of the digits at tens and one's place by 0 and keep all other digits as they are, if the digit at tens place is less than 5.
• increase the digit at the hundreds place by 1 and replace each one of the digits at the tens and one's place by 0, if the digit at the tens place is greater than or equal to 5.

(c) thousands:

• replace each one of the digits at hundreds, tens and ones place by 0 and keep all other digits as they are, if the digit at hundreds place is less than 5.
• increase the digit at the thousands place by 1 and replace each one of the digits at hundreds, tens, and ones place by 0, if the digit at the hundreds place is greater than or equal to 5.

(5) The Roman numerals with the corresponding Hindu – Arabic numerals are:

(6) To get the values of given roman numerals, we use the following rules:

• (a) If a symbol is repeated, its value is added as often as it occurs.
• If a symbol of a smaller value is written to the right of a symbol of greater value, we add its value to the value of the greater symbol.
• If a symbol of a 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 more excellent value.
• If a smaller numeral is placed between two larger digits, it is always subtracted from the larger numeral immediately following it.
• If a bar is placed over a numeral, it is multiplied by 1000.