SCHOOL ARITHMETIC

PRACTICAL BOOK

1. Measure with a ruler the length of your book. How many inches long is it? One inch is the unit of

measure.

Measure with a quart measure the water in a bucket. How many quarts are there? What is the unit of measure?

When we say we have ten apples, the unit used in counting them is one apple. One of any kind, or any group regarded as one, by comparison with which we count or measure is called a Unit.

READING AND WRITING NUMBERS

2. You have already learned to write numbers, at least to millions. You now need to learn something more about reading and writing numbers.

Our system of writing numbers by figures was first introduced into Europe by the Arabs. It is therefore called the Arabic System.

How many different figures are used in this system? Why is the zero needed?

3. Compare the numbers 1, 10, 100, 1000. How many ones does 1 express when it stands alone? When it stands at the left of a cipher? At the left of two ciphers?

In the number 22, which 2 expresses the greater value? How many times as great? In the number 222, what is the value of each 2?

Upon what does the value of each figure of a number depend?

Any figure represents ten times the value it would represent in the next place to the right.

4. In counting by ones the unit is one. In counting by tens we may regard one ten as the unit. Similarly, one hundred may be regarded as the unit for the hundreds of a number.

We speak of the different places, ones, tens, hundreds, as orders. Thus, the ones of a number are called units of the first order, or simply units; the tens are called units of the second order; the hundreds are called units of the third order; and so on.

How many units of any order make one unit of the next higher order?

How many units of any order make one unit of a higher order two places to the left?

5. When more than four figures are used to express a number, they are usually separated into groups of three as an aid in reading them. Each group is called a period. The right-hand group is called the period of units; the second group, the period of thousands; the third group, the period of millions; and so on.

6. The manner of writing numbers is shown in the following: