Whole Numbers: Learn It 1

  • Identify whole numbers and counting numbers
  • Write whole numbers in words
  • Round whole numbers
  • Add, subtract, multiply, and divide whole numbers

Identify Counting Numbers and Whole Numbers

In elementary mathematics, we frequently use the most fundamental set of numbers, which we typically employ for counting objects: [latex]1, 2, 3, 4, 5, ...[/latex] and so forth. These numbers are referred to as the counting numbers. The discovery of the number zero was a big step in the history of mathematics. Including zero with the counting numbers gives a new set of numbers called the whole numbers.

Whole and Counting Numbers

Counting numbers start with [latex]1[/latex] and continue.

 

[latex]1,2,3,4,5\dots[/latex]

 

Whole numbers are the counting numbers and zero.

 

[latex]0,1,2,3,4,5\dots[/latex]
The notation “…” is called an ellipsis, which is another way to show “and so on”, or that the pattern continues endlessly.

Modeling Numbers and Number Lines

Counting numbers and whole numbers can be visualized on a number line, as shown below. The numbers on the number line increase from left to right, and decrease from right to left. The point labeled [latex]0[/latex] is called the origin. The points are equally spaced to the right of [latex]0[/latex] and labeled with the counting numbers.

An image of a number line from 0 to 6 in increments of one. An arrow above the number line pointing to the right with the label

 

Our number system is called a place value system because the value of a digit depends on its position, or place, in a number. The number [latex]537[/latex] has a different value than the number [latex]735[/latex]. Even though they use the same digits, their value is different because of the different placement of the [latex]3[/latex],[latex]7[/latex], and the [latex]5[/latex].

Base-[latex]10[/latex] blocks provide a way to model place value. The blocks can be used to represent hundreds, tens, and ones. Notice in the image below that the tens rod is made up of [latex]10[/latex] ones, and the hundreds square is made of [latex]10[/latex] tens, or [latex]100[/latex] ones.

An image with three items. The first item is a single block with the label "A single block represents 1." The second item is a rod made up of 10 connected blocks with the label "A rod represents 10." The third item is a square made up of 100 connected blocks with the label "A square represents 100."

The image below shows the number [latex]138[/latex] modeled with base-[latex]10[/latex] blocks. We can use place value notation to show the value of the number [latex]138[/latex].

An image consisting of three items. The first item is a square of 100 blocks, 10 blocks wide and 10 blocks tall, with the label

 

An image of the expression 100 + 30 + 8. The first digit of each number is highlighted and there is an arrow from each of them to the number 138.

 

Digit Place value Number Value Total value
[latex]1[/latex] hundreds [latex]1[/latex] [latex]100[/latex] [latex]100\phantom{\rule{1 em}{0ex}}[/latex]
[latex]3[/latex] tens [latex]3[/latex] [latex]10[/latex] [latex]30\phantom{\rule{1 em}{0ex}}[/latex]
[latex]8[/latex] ones [latex]8[/latex] [latex]1[/latex] [latex]+\phantom{\rule{.5 em}{0ex}}8\phantom{\rule{1 em}{0ex}}[/latex]
        [latex]\text{Sum =}138\phantom{\rule{1 em}{0ex}}[/latex]
Use place value notation to find the value of the number modeled by the base-[latex]10[/latex] blocks shown.

An image consisting of three items. The first item is two squares of 100 blocks each, 10 blocks wide and 10 blocks tall. The second item is one horizontal rod containing 10 blocks. The third item is 5 individual blocks.

Identify the Place Value of a Digit

By looking at base-[latex]10[/latex] blocks, we saw that each place in a number has a different value. A place value chart is a useful way to summarize this information. The place values are separated into groups of three, called periods. The periods are ones, thousands, millions, billions, trillions, and so on. In a written number, commas separate the periods.

Just as with the base-[latex]10[/latex] blocks, where the value of the tens rod is ten times the value of the ones block and the value of the hundreds square is ten times the tens rod, the value of each place in the place-value chart is ten times the value of the place to the right of it.

The chart below shows how the number [latex]5,278,194[/latex] is written in a place value chart.

A chart titled 'Place Value' with fifteen columns and 4 rows, with the columns broken down into five groups of three. The header row shows Trillions, Billions, Millions, Thousands, and Ones. The next row has the values 'Hundred trillions', 'Ten trillions', 'trillions', 'hundred billions', 'ten billions', 'billions', 'hundred millions', 'ten millions', 'millions', 'hundred thousands', 'ten thousands', 'thousands', 'hundreds', 'tens', and 'ones'. The first 8 values in the next row are blank. Starting with the ninth column, the values are '5', '2', '7', '8', '1', '9', and '4'.

 

  • The digit [latex]5[/latex] is in the millions place. Its value is [latex]5,000,000[/latex].
  • The digit [latex]2[/latex] is in the hundred thousands place. Its value is [latex]200,000[/latex].
  • The digit [latex]7[/latex] is in the ten thousands place. Its value is [latex]70,000[/latex].
  • The digit [latex]8[/latex] is in the thousands place. Its value is [latex]8,000[/latex].
  • The digit [latex]1[/latex] is in the hundreds place. Its value is [latex]100[/latex].
  • The digit [latex]9[/latex] is in the tens place. Its value is [latex]90[/latex].
  • The digit [latex]4[/latex] is in the ones place. Its value is [latex]4[/latex].