Whole Numbers

Whole Numbers

The whole numbers are the counting numbers and 0. The whole numbers are 0, 1, 2, 3, 4, 5, ...

Place Value

The position, or place, of a digit in a number written in standard form determines the actual value the digit represents. This table shows the place value for various positions:

Place (underlined)	Name of Position
1 000	Ones (units) position
1 000	Tens
1 000	Hundreds
1 000	Thousands
1 000 000	Ten thousands
1 000 000	Hundred Thousands
1 000 000	Millions
1 000 000 000	Ten Millions
1 000 000 000	Hundred millions
1 000 000 000	Billions

Example:
The number 721040 has a 7 in the hundred thousands place, a 2 in the ten thousands place, a one in the thousands place, a 4 in the tens place, and a 0 in both the hundreds and ones place.

To Formed a numbers from given digits 

Given digits [4] [3] [9] [1] [3] [5]
To form the largest value, we start writing numbers in descending order. 954331
To form the smallest value, we start writing numbers in ascending order. 133459

*However if numbers given include [0], we must place it after the first number that bigger than it to form the smallest value.
example: [4] [2] [8] [0] [6] [0] => 200468 

Expanded Form (Extended Notation@Partition)

The expanded form of a number is the sum of the values of each digit of that number.We can write it in 2 type. In digit value and place value.
Example:
9836 = 9000 + 800 + 30 + 6.(digit value)
9836 = 9 thousands + 8 hundreds + 3 tens + 6 ones.(place value)

Comparing Numbers
It is good to know if one number is bigger, smaller or the same as another number! Symbols are used to show how the size of one number compares to another.
We use These Signs to compare numbers:

=	If two values are equal, we use the "equals" sign	example: 2+2 = 4
<	But if one value is smaller than another, we can use a "less than" sign.	example: 3 < 5
>	And if one value is bigger than another, we can use a "greater than" sign	example: 9 > 6

Less Than and Greater Than

The "less than" sign and the "greater than" sign look like a "V" on its side, don't they?
To remember which way around the "<" and ">" signs go, just remember:

• BIG > small
• small < BIG

The "small" end always points to the smaller number, like this:

Greater Than Symbol: BIG > small

To compare two whole numbers, first put them in standard form. The one with more digits is greater than the other. If they have the same number of digits, compare the most significant digits (the leftmost digit of each number). The one having the larger significant digit is greater than the other. If the most significant digits are the same, compare the next pair of digits from the left. Repeat this until the pair of digits is different. The number with the larger digit is greater than the other.
Example: 402 has more digits than 42, so 402 > 42.
Example: 402 and 412 have the same number of digits. We compare the leftmost digit of each number: 4 in each case. Moving to the right, we compare the next two numbers: 0 and 1. Since 0 < 1, 402 < 412. 

We use this knowledge to arrange number weather in ascending order or descending order.

Rounding Whole Numbers

When rounding whole numbers there are two rules to remember:
I will use the term rounding digit - which means: When asked to round to the closest tens - your rounding digit is the second number to the left (ten's place) when working with whole numbers. When asked to round to the nearest hundred, the third place from the left is the rounding digit (hundreds place).
Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.
Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0.

To round to the nearest ten means to find the closest number having all zeros to the right of the tens place. Note: when the digit 5, 6, 7, 8, or 9 appears in the ones place, round up; when the digit 0, 1, 2, 3, or 4 appears in the ones place, round down.

Examples:
Rounding 119 to the nearest ten gives 120.
Rounding 155 to the nearest ten gives 160.
Rounding 102 to the nearest ten gives 100.
Similarly, to round a number to any place value, we find the number with zeros in all of the places to the right of the place value being rounded to that is closest in value to the original number.

Examples:
Rounding 180 to the nearest hundred gives 200.
Rounding 150090 to the nearest hundred thousand gives 200000.
Rounding 1234 to the nearest thousand gives 1000.
Rounding is useful in making estimates of sums, differences, etc.

Example:
To estimate the sum 119360 + 500 to the nearest thousand, first round each number in the sum, resulting in a new sum of 119000 + 1000.. Then add to get the estimate of 120000.

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:
Rule One Determine what your rounding digit is and look to the right side of it. If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.
Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.
Rule Three: Some peoples prefer this method:
This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth. Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.
An example:
765.3682 becomes:
1000 when asked to round to the nearest thousand (1000)
800 when asked to round to the nearest hundred (100)
770 when asked to round to the nearest ten (10)
765 when asked to round to the nearest one (1)
765.4 when asked to round to the nearest tenth (10th)
765.37 when asked to round to the nearest hundredth (100th.)
765.368 when asked to round to the nearest thousandth (1000th) 

Tips: Method to use to round off numbers 

Example: Round off 54637 to the nearest hundreds
Step 1 : Determine number at hundreds and one digit after it.(Read as tens)
Step 2: Write number in tens at upper and below it.
Step 3: Choose number that near to the number we determine before.
54[70]0
54[63]7
54[60]0
*63 is near 60, so choose 54600.