(2009년 9월 전문강사교육 자료)

1. Whole Number System
Our system of numbers, the decimal-number system, uses 10 figures called digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. A whole number is made up of one or more digits. When a number contains two or more digits, each digit must be in the correct place for the number to have the value we intend it to have.
The place values are arranged in periods, or groups of three. The first group of three is called units, the second group of three is called thousands, the third group is called millions, and the fourth group is called billions. Commas are used to mark off these periods. The commas make larger numbers easier to read because we can locate specific place values and interpret the number more easily. Each group of three digits has a hundreds place, a tens place, and a ones place.

2. Compare Whole Numbers
Whole numbers can be arranged on a number line to show a visual representation of the relationship of numbers by size. The most common arrangement is to begin with zero and place numbers on the line from left to right as they get larger.
All numbers have a place on the number line and the numbers continue indefinitely without end. A term that is often used to describe this concept is infinity and the symbol is ∞.
Whole numbers can be compared by size by determining which of the two numbers is larger or smaller. If two numbers are positioned on a number line, the smaller number is positioned to the left of the larger number. The order relationship can be written in a mathematical statement called an inequality. An inequality shows that two numbers are not equal; that is, one is larger than the other. Symbols for showing inequalities are the less than symbol ‘<’ and the greater than symbol ‘>’.

3. Fractions with Power –of-10 Denominators as Decimal Numbers.
Numbers that are parts of a whole number are called fractions. In fraction notation, we write one number over another number
The bottom number, the denominator, represents the number of parts that a whole unit contains. The top number, the numerator, represents the number of parts being considered.
A special fraction is a fraction whose denominator is 10 or some power of 10, such as 100 or 1,000. Often the terms decimal fraction, decimal number, and decimal are used interchangeably. In fraction notation, 3 out of 10 parts is written as 3/10. On decimal notation, the denominator 10 is not written but is implied by position. A decimal point (.) separates whole-number amounts on the left and fractional parts on the right, which means we should place a decimal point (.) after the ones place. The place on the right of the ones place is called the tenths place. A decimal point is place between the ones place and the tenths place to distinguish between whole amounts and fractional amounts.
Decimal place value starts from tenths place, and then hundredths place, thousandths place, and ten-thousandths place and millionths place follow. We use cardinal numbers to represent whole number places, and ordinal numbers for decimal number places.
And so, 0.0147 should be read as “one hundred forty-seven ten-thousandths. But people usually take the informal way not to be miscommunicated and read this “point zero one four seven or zero point zero one four seven” instead.

4. How to Rounding a Number
(1) Locate the digit that occupies the rounding place.  Then examine the digit to the immediate right.
(2) If the digit to the right of the rounding place is 0,1,2,3,or 4, do not change the digit in the rounding place. If the digit to the right of the rounding place is 5,6,7,8, or 9, add 1 to the digit in the rounding place.
(3) Replace all digits to the right of the digit in the rounding place with zeros if they are to the left of the decimal point. Drop digits that are to the right of the digit in the rounding place and also to the right of the decimal point.

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