![]() ![]() ![]() We have now then constructed the names and the numerals for all the numbers 1 through 999. In this way we name the numbers 100 through 999, and construct their numerals. , Three Hundred Ninety-eight (398), Three Hundred Ninety-nine (399). To write their numerals, successively replace the two 0's of the lower Hundred with the numerals of the first ninety-nine numbers.įor example: Three Hundred One (301), Three Hundred Two (302), Three Hundred Three (303). To compose the numbers between two consecutive Hundreds - between 300 and 400, for example - successively add the first ninety-nine numbers to the lower Hundred. Numbers between two consecutive Hundreds. Upon letting One Hundred be the unit, we count those Hundreds and name them as follows: 1 Hundred A collection of ten Tens form the number One Hundred. We have now named the numbers 1 through 99, and constructed their numerals. To write their numerals, successively replace the 0 of the lower Ten with the first nine numbers. To compose the numbers between two consecutive Tens - between 30 and 40, for example - successively add the first nine numbers to the lower Ten. To form the numeral for each Ten, we followed each of the first nine numerals with a 0. On counting the Tens, here are their names and their numerals: 1 Ten The name of the number one more than Nine is Ten: 10. Your five fingers did not come about by adding one to four. Apart from that, each number is an autonomous whole. It links the sequence of the names with their cardinality: how many. We have added one to Four to produce Five. We say that we have "added one" to the previous number. ![]() Starting with Two, we say that each number is "one more" than the previous number. Here is the sequence of the first nine counting-names and their numerals: One For that is how we learn the sequence of the names. Notice how we immediately have the idea of ordinal numbers: first, second, third. The child to grasp the idea of a number, and thusĮventually represent the number with a symbol. The thing is the number.Ĭhildren often learn the concepts of arithmetic with manipulatives, which are actual numbers - physical units - such as matchsticks or blocks. Since it is with those numerals-1, 2, 3, 4-that we do written calculations, it has become common to call the numerals themselves "numbers." But like any symbol it is not the thing to which it refers. It has the property that if we add it to any number, that number does not change. "Five" is the English word.Ġ (zero) is also called a whole number. For it was the Arab mathematicians who introduced them into Europe from India, where their forms evolved. 'V' is the Roman numeral for this number: The student is no doubt familiar with Roman numerals. The symbols for the counting-numbers - 1, 2, 3, 4, 5 - are called numerals. (They are also called the natural numbers. We call them the counting-names sometimes the counting-numbers. As you surely know, the English names for the whole numbers are "One, two, three, four" and so on. To do arithmetic, the numbers obviously must have names and symbols. And so we speak of whole number arithmetic and whole number numeration it does not include fractions or decimals. We measure things that are not whole numbers, therefore we have fractions and decimals. Similarly for measuring time, weight, temperature whatever we cannot count.Ī whole number is composed of distinct, indivisible units. We then relate the length we are measuring to that unit. To measure length, for example, we must adopt a length that we will call one: one meter, one foot, one mile. To measure we must adopt a unit of the same kind as that which we are measuring. Counting is determining how many of those units are contained in the whole. "One dollar, two dollars, three dollars." We can only count things of the same kind, that is, that have the same name. That means it is based on what are called the powers of 10. The current system, which is in worldwide use, is the decimal system. ![]() Numeration is the foundation upon which arithmetic is built and expressed. Arithmetic is the art of skillful calculation.įirst, we need a plan for naming numbers with words, and then for writing them with symbols. A RITHMETIC is the discipline that studies numbers the relationships between them and the operations with them. ![]()
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