Chapter Notes and Summary
• Notation : Writing a number in figures is called notation.
• Numeration : Writing a number in words is called numeration.
• Digits or figures : 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are called digits or figures.
• Numeral : A group of digits, denoting a number, is called a numeral.
• Comparing numbers : Two given numbers can be compared by counting their number of digits. number having more digits is greater than a number having less digits.
• Ascending order : In ascending order, numbers or quantities are arranged from lowest to largest.
• Descending order : In descending order, numbers or quantities are arranged from highest to lowest.
• In Hindu-Arabic place value system, we start from extreme right as; ones, tens, hundreds, thousands, ten thousands, lakh, ten lakhs etc.
• Periods : Crore, lakh, thousand and hundred are known as periods.
• Separating periods in Hindu-Arabic system : Crore, lakh thousands (hundreds + tens + ones).
• Face value of a digit : face value of a digit remains as it is, whatever place it may be occupying in place value chart.
• Place value of a digit : place value of digit in a numeral depends upon place it occupies in place value chart.
• International system of numerations :
Periods Billions Millions Thousands Ones Ten billion Billion Hundred million Ten millions Million Hundred thousands Ten thousands Thousands Hundreds Tens Ones T Ar Ar TCr Cr TL L T Th Th H T O
• 1 million = 10 lakh
• 10 million = 1 crore
• 1000 million = 100 crore or 1 arab
• number with less digits is less than number with more digits.
• units kilo is greatest and milli is smallest. Also, kilo shows 1000 times greater whereas milli shows 1000 times smaller and centi shows 100 times smaller.
• 1 kilometre = 1000 metre
• 1 kilogram = 1000 grams
• 1 metre = 10 decimetre = 100 centimetre = 1000 millimetre
• 1 gram = 10 decigram = 100 centigram = 1000 milligram.
• 1 litre = 10 decilitre = 100 centilitre = 1000 millilitre.
• In above figure, each unit has difference of 10.
i.e., 1 kilometre = 10 hectometre and 1 kilometre = 10 × 10 decametre
• Estimation means approximating a quantity to an accuracy required.
• Roman numbers :
Roman Numeral I V X L C D M Hindu-Arabic Numeral 1 5 10 50 100 500 1000
• If a bar is places over a numeral, it is multiplied by 1000. Thus V = 5000, X = 10000 etc.
• Repetition of a Roman numeral means addition.
Note : (i) Only I, X, C, M can be repeated
(ii) V, L and D are never repeated.
(iii) No symbol (Roman numeral) can be repeated more than 3 times.
• A smaller numeral written to right of larger numeral is always added to larger numeral.
• A smaller numeral written to left of a larger numeral is always subtracted from larger numeral.
Note : (i) V, L and D are never subtracted.
(ii) I can be subtracted from V and X only.
(iii) X can be subtracted from L and C only.
(iv) C can be subtracted from D and M only.
• When a smaller numeral is placed between two larger numerals, it is always subtracted from larger numeral immediately.