How a Place Value Chart Reveals a Digit’s Position in a Number

This chart shows which part of a number corresponds to which category of values. zizou7 / Shutterstock

The concept of place values is fundamental to mathematics and the number system, particularly when you’re dealing with whole numbers and decimal numbers. A place value chart is an essential tool that can help students visualize the position of each digit in a number and understand its actual value within the context of the number.

For example, the place value system could help you decipher which digit in a large whole number is in the ones, tens, hundreds, thousands, millions or billions place. Or it could help you determine which digit to the right of the decimal point in a very small decimal number is in the tenths, hundredths, or thousandths place.

Let’s take a closer look at what a place value chart is and explore a few suggestions for using one.

What Is a Place Value Chart?

A place value chart (also called a decimal place value chart or place value table) is a visual tool that helps students visualize place value in numbers. It does this by illustrating the position of each digit in a number, showing how the value of the digit depends on its place within the number.

Place value charts are divided into two main parts: the whole number part and the fractional part. These parts are separated by a decimal point, which plays a crucial role in distinguishing between whole numbers and decimal fractions.

Distinguishing Face Value From Actual Value

Using a place value chart helps students disregard each digit’s face value and instead consider how it contributes to the number’s overall value.

For example, consider the number 3,912.487. Students can place the digit 3 in the thousands place, 9 in the hundreds place, 1 in the tens place, 2 in the ones place, 4 in the tenths place, 8 in the hundredths place and 7 in the thousandths place.

The chart clarifies the difference between the face value of a digit and its actual value in a number. In the above example, the place value of 4 is 0.4 — but in 4,815, the place value of 4 is 4,000.

The Whole Number Part of a Place Value Chart

The whole number part of a place value chart deals with everything to the left of a decimal point in a number or decimal number.

Starting from the right, the first column on a place value chart with no decimal point is the ones place, followed by the tens place, hundreds place, thousands place, ten thousands place, hundred thousands place and extending up to the billions place or beyond.

Each position to the left increases the value of the digit ten times over the position to its right. For example, in the number 5,674, the digit 4 is in the ones column, 7 in the tens column, 6 in the hundreds column and 5 in the thousands place.

The Fractional Part of a Place Value Chart

The fractional part of a place value chart is useful when you are working with place values in a decimal number. Digits to the right of the decimal point represent the tenths place, hundredths place and thousandths place, among others. Each position to the right decreases the value of the digit ten times, compared to the position to its left.

By following place value chart rules, students can learn how the value of a digit decreases as it moves further to the right of the decimal point.

Using Place Value Charts in Education

Decimal place value charts are specifically designed to help students write numbers that include a decimal point and to help them better understand the number system in general. These charts help them to recognize how the decimal point represents a boundary between the whole number part and the fractional part of a number.

Teachers can employ place value charts as math resources when they’re teaching children about place values, such as when they’re introducing the students to very small or very large numbers and decimal numbers.

By using charts, children can practice writing numbers correctly and gain confidence in their ability to work with different numbers. For instance, a teacher might use a printable place value chart during lessons or provide practice questions that encourage students to place digits in the correct columns.

We created this article in conjunction with AI technology, then made sure it was fact-checked and edited by a HowStuffWorks editor.

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