HOW THE USE OF NUMBERS BEGAN
Many thousands of years ago this was a world without numbers. Nobody missed them. Everyone knew just what belonged to him and what not. If a cow was missing, the owner knew it was gone, not by counting cows, but for the same reason your mother would know if you did not come home for dinner.
But some people acquired more and more property. They would count1 one cow, two cows, three cows; one vase, two vases, three vases; always one, two, three or more of something they owned or saw.
How far we have advanced from the time of our ancestors! Today, using numbers, numerals and mathematics, man builds bridges, skyscrapers, flies off the earth like a bird, even measures the distance to the moon and the brightness of the light given off by the firefly. But just as important though not so exciting, is that he can tell the time, pay the grocer, count the runs in a baseball game and use the same numbers in many different ways in everyday life.
So you see, mathematics and numbers, from simple arithmetic to complex algebraic and geometric calculations, are important to life in our time.
Roman Numerals. The Romans used seven capital letters to represent numbers. They mixed them together to form many different combinations.
The Roman system of numbers is based upon the letters, I, V, X, C, D and M.
This is what each letter represents:
Roman Numeral I V X L С D M
Hindu-Arabic Numeral 1 5 10 50 100 500 1000
Notes:
1 they would count — вони зазвичай рахували
2 just as important — так само важливо
EXERCISES
I. Read the following words paying attention to the pronunciation:
acquire, advance, ancestors, skyscrapers, firefly, exciting, brightness, light, algebraic, geometric.
II. Form nouns of the following words:
to count, to advance, to use, to build, to fly, to pay, to represent.
III. Form adjectives of the following words by adding the
suffixes -ful, -less, -able and translate them:
use, need, reason, count, represent.
IV. Answer the following questions:
1. When did people begin to count?
2. For what purposes do we use numbers?
3. Why are mathematics and numbers important?
4. What letters did the Romans use to represent numbers?
V. Translate into Ukrainian:
Primitive man knew only ten number-sounds. The reason was that he counted in the way a small child counts today, one by one, making use of his fingers. The needs and possessions of primitive man were few: he required no large numbers.
When he wished to express a number greater than ten he simply combined certain of the ten sounds connected with his fingers. Thus, if he wished to express "one more than ten" he said "one-ten" and so on.
VI. Make up sentences of your own using the words and expressions given below:
acquire, property, advance, measure, important, calculations, for the same reason, just as important, to make use of, in everyday life, in the same way, in a different way.
HOW WE READ AND WRITE NUMBERS
To make it easier to read large numbers, we separate the figures of the numbers by commas into groups of three, counting from right to left. Each group is called a period and has its own name.
The system of numbers we use, called Arabic system, is a decimal system: that is, it is based on tens. In this system, the value a digit represents is determined by the place it has in the number; if a digit is moved to the left one place, the value it represents becomes ten times as great.
Zero in the decimal system is a "place-holder"; in the number 30, the zero shows that 3 has been moved to the left one place, thus counting tens instead of ones. The place value in numbers is shown below:
682,000,000,000 847,000,000 136,000 592
Billions Millions Thousands Ones
These numbers are read: six hundred eighty-two billion, eight hundred forty-seven million, one hundred thirty-six thousand, five hundred and ninety-two.
682,000,000,000 847,000,000 136,000 592
Billions Millions Thousands Ones or Units
4 periods 3 periods 2 periods 1 period
Rule to Remember: a) All periods of a number contain three digits, or places (the first period on the left may or may not), b) Zero is used as a place-holder.
Average. When we want to find a single number that will represent all the numbers in a group of unequal numbers or quantities we find the average (or arithmetic mean).
To find the average of a group of unequal numbers, we add the numbers and then divide their sum by the number of addends.
Notes:
1 to make it easier to read — для того, легше легче читати
2 is determined by the place — визначається місцем
3 ten times as great — в десять разів більше
EXERCISES
I. Read the following words paying attention to the pronunciation:
to separate, period, system, zero, average, digit, unequal.
II. Form nouns of the following verbs:
to read, to count, to move, to place, to contain, to find, to determine, to represent.
III. Make up sentences of your own using the words and expressions given below:
quantity, unequal, sum, to make it easier to read, to separate the figures of the number, to be determined by, ten times as great, ten times as small.
IV. Answer the following questions:
1. Why do we separate the figures of the numbers by commas?
2. How is each group of three figures called?
3. How is the system of numbers we use called?
4. How many digits does a period of a number contain?
5. How do we find the average of unequal numbers?
V. Translate into Ukrainian:
Our present-day number-symbols are Hindu characters. It is important to notice that no symbols for zero occur in any of these early Hindu number system. They contain symbols for numbers like twenty, forty, and so on. A symbol for zero had been invented in India. The invention of this symbol for zero was very important, because its use enabled the nine Hindu symbols 1, 2, 3, 4, 5, 6, 7, 8 and 9 to suffice
for the representation of any number, no matter how great. The work of a zero is to keep the other nine symbols in their proper place.
VI. Translate into English:
Десяткова система нумерації виникла в Індії. Згодом її стали називати «арабською», тому що вона була перенесена в Європу арабами. Цифри, якими ми тепер користуємося, теж називаються арабськими. У цій системі особливо важливе значення має десять, і тому система носить назву десяткової системи нумерації. Щоб легше читати багатозначні числа, ми відокремлюємо (separate) цифри в них комами по три в групі. Групу з трьох цифр ми називаємо періодом.
