# Decimal Arithmetic

The decimal numbering system uses ten symbols called digits, each digit representing a number. These symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The symbols are known as the numbers zero, one, two, three, etc. By using combinations of 10 symbols, an infinite amount of numbers can be created. For example, we can group 5 and 7 together for the number 57 or 2 and 3 together for the number 23. The place values of the digits are multiples of ten and given place titles as follows: Numbers in the decimal system may be classified as integers or fractions. An integer is a whole number such as 1, 2, 3, . . . 10, 11, . .  A fraction is a part of a whole number, and it is expressed as a ratio of integers, such as 1/2, 1/4, or 2/3. An even integer, is an integer which can be exactly divided by 2, such as 4, 16, and 30. All other integers are called odd, such as 3, 7, and 15. A number can be determined to be either odd or even by noting the digit in the units place position. If this digit is even, then the number is even; if it is odd, then the number is odd.Numbers which end in 0, 2, 4, 6, 8 are even, and numbers ending in 1, 3, 5, 7, 9 are odd. Zero (0) is even.

Examples:

Determine whether the following numbers are odd or even: 364, 1068, and 257.

Solution:

1. 364 is even because the right-most digit, 4, is an even number.

2. 1068 is even because the right-most digit, 8, is an even number.

3. 257 is odd because the right-most digit, 7, is an odd number.

This module explains the basic operations using decimals. This entire number system  contains another method of parts of a whole, and it is known as decimal fractions. It is very important that students take the time  to really understand  decimal arithmetic. In this chapter, students will learn how to:

Rounding off Decimals

Subtracting Decimals

Multiplying Decimals

Dividing Decimals

Comparing Decimals

Converting Fractions to Decimals

Converting Decimals to fractions

Write Decimals as Mixed Numbers