Place Value and Names for Whole Numbers

Learning Objectives

• Find the place value of a digit in a whole number.
• Write a whole number in words and in standard form.
• Write a whole number in expanded form.

Mathematics involves solving problems that involve numbers. We will work with whole numbersAny of the numbers `0`, `1`, `2`, `3`, and so on. , which are any of the numbers `0, 1, 2, 3`, and so on. We first need to have a thorough understanding of the number system we use. Suppose the scientists preparing a lunar command module know it has to travel `382,564` kilometers to get to the moon. How well would they do if they didn’t understand this number? Do you think it would make more of a difference if the `8` was off by `1` or if the `4` was off by `1`?

In this section, you will take a look at digits and place value. You will also learn how to write whole numbers in words, standard form, and expanded form based on the place values of their digits.

A digitOne of the symbols `0`, `1`, `2`, `3`, `4`, `5`, `6`, `7`, `8`, or `9`. is one of the symbols `0, 1, 2, 3, 4, 5, 6, 7, 8`, or `9`. All numbers are made up of one or more digits. Numbers such as `2` have one digit, whereas numbers such as `89` have two digits. To understand what a number really means, you need to understand what the digits represent in a given number.

The position of each digit in a number tells its value, or place valueThe value of a digit based on its position within a number. . We can use a place-value chartA chart that shows the value of each digit in a number. like the one below to easily see the place value for each digit. The place values for the digits in `1,456` are shown in this chart.

In the number `1,456`, the digit `1` is in the thousands place. The digit `4` is in the hundreds place. The digit `5` is in the tens place, and the digit `6` is in the ones place.

As you see above, you can tell a digit’s value by looking at its position. Look at the number of digits to the right of the digit, or write your number into a place-value chart, with the last digit in the ones column. Both these methods are shown in the example below.

The standard formA way to write a number using digits. For example, thirty-two is written in standard form as `32`. of a number refers to a type of notation in which digits are separated into groups of three by commas. These groups of three digits are known as periodsEach group of three digits in a number separated by a comma.. For example, `893,450,243` has three periods with three digits in each period, as shown below.

Let’s examine the number of digits and periods in a greater number. The number of body cells in an average adult human is about one hundred trillion. This number is written as `100,000,000,000,000`. Notice that there are `15` digits and `5` periods. Here is how the number would look in a place-value chart.

You are now familiar with the place values of greater numbers, so let’s examine a problem that involves converting from standard form to a word name.

We often use word names to write numbers. A word name for `42` is “forty-two.” The total number of weeks in a year, `52`, is written as “fifty-two.”

For whole numbers with three digits, use the word “hundred” to describe how many hundreds there are in the number. For example, for the number of days in a normal year, `365`, the digit `3` is in the hundreds place. The word name for the number is “three hundred sixty-five.”

For whole numbers with four digits, begin the name with the number of thousands, followed by the period name, as in the example below.

For word names of greater numbers, begin at the left with the greatest period. For each period, write the one- to three-digit number in the period, and then the period name. See the example below.

When converting word names to standard form, the word “thousand” tells you which period the digits are in. See the example below.

Below is an example with a number containing more digits. The words “million” and “thousand” tell you which periods the digits are in. The periods are separated by commas.

Some numbers in word form may not mention a specific period. For example, three million, one hundred twelve written in standard form is `3,000,112`. Because the thousands period is not mentioned, you would write three zeros in the thousands period. You can use a place-value chart to make it easier to see the values of the digits. See the example below.

Sometimes it is useful to write numbers in expanded formA way to write a number as a sum of the value of its digits. For example, thirty-two is written in expanded form as `30 + 2`, or `3` tens `+` `2` ones, or `(3 * 10)+(2 * 1)`. . In expanded form, the number is written as a sum of the value of each digit.

You can also use a place-value chart to help write a number in expanded form. Suppose the number of cars and pick-up trucks in the U.S. at this very moment is `251,834,697`. Place this number in a place-value chart.

Whole numbers that are greater than `9` consist of multiple digits. Each digit in a given number has a place value. To better understand place value, numbers can be put in a place-value chart so that the value of each digit can be identified. Numbers with more than three digits can be separated into groups of three digits, known as periods. Any whole number can be expressed in standard form, expanded form, or as a word name.