Sets of Numbers

Counting numbers start from 1 and continues to infinity, for example, 1, 2, 3, 4, 5, 6, ...
Whole numbers start from 0 and continues to infinity, for example, 0, 1, 2, 3, 4, 5, 6, ...
Even numbers are numbers when divided by 2 doesn't leave a remainder. In the one's place, even numbers always have either of the following digits: 0, 2, 4, 6, 8
Odd numbers are numbers when divided by 2 have a remainder which is 1. In the one's place, odd numbers always have either of the following digits: 1, 3, 5, 7, 9
Factors - a factor of a given number is any number when multiplied results in the given number, for example,

1 x 12 = 12 2 x 6 = 12 3 x 4 = 12

Here, the factors of 12 are { 1, 2, 3, 4, 6, 12} because all these numbers can be multiplied by another number to give 12.

One (1) and the given number are always factors. Factors are always a finite set.

Multiples - a multiple of a given number is any number that can be divided evenly by the given number. For example,

18 / 3 = 6 27 / 3 = 9 3 / 3 = 1 12 / 3 = 4

Here, the multiples of 3 are {3, 12, 18, 27}

Prime Numbers are numbers that have 2 factors only, 1 and the number itself. Two (2) is the only number that is prime and also even.
Composite Numbers are numbers that have more than 2 factors. One (1) is not prime and is not composite because it has 1 factor only which is 1.

Face Value

The face value of a digit is the actual name of the digit as seen in a given number, for example:

in the number 345,107, the face value of the digit in bold is 4 because 4 is the digit we actually see.

Place Value

The place value of a digit is the position held by that digit in a number. Each digit in a number can only take 1 position or place value. Therefore, if a number has 5 digits then automatically it has 5 place values. A number with 3 digits has 3 place values and so on. Some of the place values you should be familiar with are shown on the place value chart below. Can you write all the numbers in words?

Value

The value of a digit is how much that digit is worth. To calculate the value of a digit, simply multiply the digit's face value by its place value. For example, in the number 23,578, the 5 is in the hundreds place. Therefore, its value is 5 x 100 = 500. Likewise, the digit 2 is in the ten thousands place, so its value is 2 x 10,000 = 20,000.

Standard Notation

Standard notation is a special way of writing numbers in which the value of all digits of that number are added together. Look at the examples below.

67 = (6 x 10) + (7 x 1) 367 = (3 x 100) + (6 x 10) + (7 x 1)

= 60 + 7 = 300 + 60 + 7

254,367 = (2 x 100,000) + (5 x 10,000) + (4 x 1,000) + (3 x 100) + (6 x 10) + (7 x 1)

= 200,000 + 50,000 + 4,000 + 300 + 60 + 7

Rounding to the Nearest 10

To round to the nearest 10, first examine the digit in the ones place. If this digit is less than 5, keep the digit in the tens place while the digit in the ones place becomes a zero. On the other hand, if the digit in the ones place is 5 or more, add 1 to the digit in the tens place while the digit in the ones place becomes zeroes.

Rounding to the Nearest 100

To round to the nearest 100, first examine the digit in the tens place. If this digit is less than 5, keep the digit in the hundreds place while the digits in the tens and ones places become zeroes. On the other hand, if the digit in the tens place is 5 or more, add 1 to the digit in hundreds place while the digits in the tens and ones places become zeroes.

Rounding to the Nearest 1000

To round to the nearest 1000, first examine the digit in the hundreds place. If this digit is less than 5, keep the digit in the thousands place while the digits in the hundreds tens and ones places become zeroes. On the other hand, if the digit in the tens place is greater than 4, add 1 to the digit in thousands place while the digits in the hundreds, tens and ones places become zeroes.