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289 MISCELLANEOUS EXERCISES
1. A Unit is a single thing, or one. Thus, A dollar is a unit, an apple is a unit, etc.
2. Quantity is any thing that can be measured, or computed. Thus,
Distance is quantity, since it can be measured, so as to be named miles, rods, etc.
3. A Number is a unit, or a collection of anits of tho same kind.
One, two, three, four, etc., which show how many units there are of any quantity, express numbers.
4. The Unit of a Number is one of that number. Thus,
One dollar is the unit of three dollars, and one the unit of five.
5. Like Numbers are such as have the same unit. Thus, Five dollars and seven dollars are like numbers.
6. A Concrete Number is a number in which some kind of unit is named. Thus,
, Two books, five days, seven dollars, are concrete numbers.
What is a Unit? A Quantity ? A Number? The Unit of a Number? Like Numbers? A Concrete Number?
7. An Abstract Number is a number in which no. particular kind of unit is named. Thus,
Two, five, in which no particular unit is named, are abstract numbers.
8. An Operation is a process performed with numbers.
A Rule is a direction for performing an operation. 12. An Example is an application of a rule. 13. An Exercise is a lesson for practice. 14. Arithmetic is the science of numbers and the art of
15. Practical Arithmetic treats of the methods of applying numbers to practical or business purposes.
NOTATION AND NUMERATION.
16. Notation is the method of writing numbers.
18. Figures are certain marks or characters used to express numbers.
The method of expressing numbers by figures is called the Arabic, because it was used by the Arabs.
Ten different figures are used in expressing numbers.
What is an Abstract Number? What is an Operation ? An Answer! A Solution ? A Rule? An Example ? An Exercise ? Arithmetic ? Practical Arithmetic ? Notation ? Numeration ? What are Figures ? What is the method of expressing numbers by figures called? Why se called?
Figures as written.
Names, or Figures
Figures Figures value denoted. as printed.
value denoted. as printed. as written Cipher, 0
9 19. The figures 1, 2, 3, 4, 5, 6, 7, 8, 9, are called signif cant figures, because each signifies, or stands for, the number, which its name denotes.
t'he figure 0, or cipher, is sometimes called zero, or naught, because, when used alone, it stands for no number. Thus,
0 dollars means no dollars.
No number higher than nine can be expressed by a single figure, but by combining figures all other numbers may be denoted.
UNITS, TENS, HUNDREDS.
20. In naming numbers, nine units and one more are regarded as forming a single group, or collection, called TEN.
One ten and one are called ELEVEN; one ten and two, TWELVE; one ten and three, THIRTEEN; one ten and four, FOURTEEN; etc., “teen” meaning “and ten."
Two tens are called TWENTY; three tens, THIRTY; four tens, FORTY ; etc., “ty” meaning "tens.”
21. To express ten, twenty, thirty, etc., we write 1, 2, 3, etc., denoting the number of tens, to the left of 0. Thus, Ten, 10 | Forty, 40 Seventy,
70 Twenty, 20 Fifty, 50 | Eighty,
80 Thirty, 30 Sixty, 60 Ninety,
Why are 1, 2, 3, etc., called significant figures ? What is the cipher sometimes called? How high numbers can be expressed by a single figure ? How may
all numbers be denoted ? What name is given to nine and one more? To ten and one, etc. ? How do we express ten, twenty, thirty, etc."
where 0 denotes the absence of ones, or units of the first order, and makes other figures express tens, or units of the second order.
22. To express the whole numbers intermediate between ten and twenty, twenty and thirty, thirty and forty, etc., we write the figures denoting the number of tens, to the left of 1, 2, 3, etc., expressing the ones, or units of the first order. Thus, Eleven,
11 Sixteen, 16 | Twenty-two, 22 Twelve,
12 Seventeen, 17 Twenty-three, 23 Thirteen,
13 Eighteen, 18 Twenty-four, 24 Fourteen, 14 Nineteen, 19 Twenty-five, 25 Fifteen, 15 | Twenty-one,
21 Twenty-six, 26 and so on.
23. Ten tens are called ONE HUNDRED, which forms a unit of the third order, and is written 100.
Therefore, to express one hundred, two hundred, three hundred, etc., we write the figure denoting their number with two ciphers at the right. Thus,
200 300 400 500
600 700 800 900
24. In expressing a whole number by three figures, we place the figure denoting the hundreds in the third, the figure denoting the tens in the second, and the figure denoting the units in the first place from the right. Thus,
Two hundred and sixty-three, or 2 hundreds, 6 tens, and 3 units, is written 263.
Five hundred and seven, or 5 hundreds, 0 tens, and 7 units, is written 507.
How do we express numbers between ten and twenty? What are ton tens called ? What forms a unit of the third order? In writing a number expressed by three figures, how are the figures placed ?