Decimal place value

Decimal Place Value: Teaching About Place Value and Decimals

When students learn about decimal place value, they learn how to compare decimals, and are able to arrange them in ascending or descending order. They also gain fluency in rounding off decimals.

Students may initially find decimal place value concepts confusing and mix up the tenths with tens or hundredths with hundreds, but don’t despair! If you’re teaching this, we’ve outlined a few cool teaching strategies that will help make the learning process smooth and fun! Read on!

A teacher holding books, standing in front of a white board

Strategies to Teach Decimal Place Value

What Are Decimals?

Students are already familiar with decimals and what they represent, but it’s always good to refresh their memory. So start off your lesson on decimal place value by defining a decimal as a number that consists of a decimal point, followed by digits whose value is smaller than one.

Write a few examples on the whiteboard, such as 2.5, 1.23, 0.52, 0.002, etc. Ask students to identify the whole number part and the fractional part in each given decimal.

Decimal Place Value

Point out that the digits that are after the decimal point represent the decimal places. The decimal places also indicate the position of the digits. Draw a decimal on the whiteboard to illustrate this:

Define tenths as the first digit to the right of the decimal point, hundredths as the second digit to the right of the decimal point, and so on. Feel free to also check out our article on place value, in addition to our articles on tenths and hundredths.

Explain that we can read and write out a particular digit’s exact value by locating its place value. For example, to find the value of 7 in 9.078, we’ll locate the place value of 7. In this case, it’s hundredths. Hence, the value of 7 is ‘7 hundredths’.

Comparing Decimals Using Place Value Charts

Explain that we can compare decimals with the help of place value charts. Students have already used place value charts for whole numbers, so point out that now we’ll simply adjust these charts to use them for decimals to show the place of digits in numbers.

For example, let’s say we want to compare 4.859 and 4.869. Draw a place value chart on the whiteboard and demonstrate to students how to place each digit in the correct place. Using our place value knowledge, we’ll need to draw a ones, tenths, hundredths, and thousandths place:

Explain that we can start comparing the digits of 4.859 and 4.869 beginning from the leftmost place value and we’ll stop once we find digits that aren’t equal. Since both decimal numbers have the same digit in the ones place (4), we’ll move on to the next place value.

Here, it’s clear that both numbers have the same digit in the tenths place as well (8), while the hundredths digits are different. In the first decimal number, we have 5 in the hundredths place, and in the second one, we have 6 in the hundredths place.

So comparing the hundredths digit of the two decimal numbers, we can say that ‘5 hundredths is less than 6 hundredths’. Thus, this means that 4.869 is greater than 4.859.

Comparing Decimals by Inspection

Comparing decimal numbers with the help of a place value chart is a great way to learn how to compare decimal numbers. But once students are comfortable with place value charts, you can also omit them and compare decimal numbers by inspection.

Point out that with this method, just like with place value charts, we’ll start at the leftmost digit. If the digits on the same place value are the same, all we need to do is to move on to the next place value until we can finally compare the digits.

So we’ll inspect the digits in each place value simultaneously until we can find the greater digit. Highlight that we must always start inspecting each digit from left to right. Provide an example on the whiteboard of comparing decimals by inspection.

For instance, let’s say we want to determine if 12.475989 is greater than or less than 12.455966. We can even arrange the two numbers one under the other to help visualize the comparison of each digit:

Starting from the leftmost place value, the digits in the tens place are the same (1 = 1), the digits in the ones place are also the same (2 = 2) and in the tenths place, they’re equal again (4 = 4). It’s only in the hundredths place that we notice that we have two different digits, 7 and 5.

Since 7 is greater than 5, we can conclude that 12.475989 is greater than 12.475966.

Arranging Decimals by Inspection

Once students are confident in their knowledge of comparing decimals, point out that we can also use inspection to arrange several decimals in ascending (from least to greatest) or descending (from greatest to least) order.

For instance, let’s say we want to arrange 4.5104, 4.5014, 4.5041, and 4.5140 in ascending order. Explain that we’ll start by writing the four decimal numbers one under the other to help us visualize the comparison, just like we did when we compared two decimal numbers:

Explain that the digits in the ones place are the same, just like the digits in the tenths place. We can observe that 4.5014 and 4.5041 would be the smaller decimals and 4.5104 and 4.5140 would be the two greater decimals since they have a larger value on their hundredths place.

Add that 4.5014 and 4.5041 have the same digit in the hundredths place (0). Since they are the smaller numbers, we can first decide which among the two is the smallest by examining the thousandths digit, as we established that the digits in the hundredths place are the same.

It’s clear that 4.5014 has the smallest thousandths value, followed by 4.5041 because 4 is greater than 1. Now, we can take a look at the remaining decimal numbers and decide which one should come next.

Between the decimal numbers 4.5104 and 4.5140, the former has a smaller thousandths value compared to the latter (4 is greater than zero). Therefore, arranging the given numbers from least to greatest, we’ll form this ascending order:

4.5014, 4.5041, 4.5104, 4.5140

Rounding Decimals Using Place Value Charts

Explain to students that we can use our knowledge of place value to round decimals. Why would we need to round decimals? Because some calculations are done more easily when decimals are rounded off a certain level of certainty (or on the required place value).

For instance, one of the most commonly used decimals in geometry is rounded off to its hundredths place, so that it’s easier for us to find the areas and length of circles and arcs. This is of course the number π.

Example: Rounding off π

Explain to students why π is equal to 3.14 when rounded off to the nearest hundredths. You can start by constructing a place value chart for the first five digits of π on the whiteboard:

Explain that when we’re rounding off a decimal number, we need to follow certain steps:

  • We’ll locate the rounding digit represented by the given place value (in this case this is the digit in the hundredths place, as we wanted to round off π to the nearest hundredths). Then, we’ll inspect the digit to its right (in this case, this is 1).
  • If the digit to its right is less than 5, we’ll retain the value of the digit we want to round off, and we’ll remove the remaining decimal places to the right after the rounding digit.
  • If the digit to its right is equal to or greater than 5, we’ll add 1 to the digit we want to round off.

Point out that, in the example at hand, the digit to the right of 4 is 1, so we’ll just retain the value of 4. To determine the final value of the decimal when rounded off to the nearest hundredths, we remove the remaining decimal places to the right after the hundredths place.

This is why π equals approximately 3.14 when rounded off to the nearest hundredths.

Rounding Decimals Without Place Value Charts

Once students are comfortable with using place value charts in rounding decimals, they can also master the process without any charts. They would of course still rely on their place value understanding.

Provide an example of how this would look like in practice. For instance, let’s say we want to round off 5.67879 to the nearest thousandths. Add that to round off this decimal, we can follow the steps enumerated above.

Point out that first, we’ll locate the digit found in the indicated place value, that is, the digit in the thousandths place. So this is 8. Then, we’ll inspect the digit to the right of 8. This is 7. We’ll add 1 to 8 since 7 is greater than 5. Finally, we’ll delete the remaining digits to the right

Thus, 5.67879 rounded off to the nearest thousandths is 5.679.

Additional Resources:

If you have the technical possibilities in your classroom, you can also enhance your lesson on teaching about place value and decimal numbers with diverse multimedia materials, such as videos.

For example, this video contains simple guidelines and a practical example on how to compare decimals, where it’s illustrated how we can compare the following two decimals: 156.378 and 156.348.

Then, use this fun video to introduce students to the concept of rounding decimals and to demonstrate how we carry out decimal rounding. This video is also a great resource with a worked example on how to round 9.564 to the nearest tenth.

Activities to Practice Decimal Place Value

Decimal Place Value Game

This is a great starting game when teaching decimal place value and ordering and rounding decimal numbers, as it boosts your students’ understanding of decimal place value. The only materials needed are technical devices that the students in your class can use to play the game on.

Pair students up. Explain to them that they are presented with a decimal number in each exercise in the game, as well as a place value chart. They have to place each digit of the decimal number in the correct position in the place value chart.

If they do this correctly, they score coins. In the end, students in each pair compare their scores. The winner is the person with the highest score, that is, the person with the most coins. Play as many rounds as time allows it.

Arranging Decimals Balloon Game

This is a fun game that will provide the opportunity for students to practice comparing decimals, as well as arranging them in ascending order by applying their decimal place value knowledge. To use this game in your classroom, you’ll need paper, markers, and scissors.

Draw balloons on the paper and write one decimal inside each balloon. Create as many balloons as needed, taking into consideration that you’ll need at least 5 per group. Cut out the balloons with the scissors.

Divide students into small groups of 3, 4 and hand out the balloons and one marker per group. Tell students that they need to compare the decimals in the balloons they received and arrange them in ascending order. In the end, they should color the balloon with the greatest decimal.

Provide some 10 minutes for students to complete the comparisons. Then, ask each group to present how they arranged the balloons in ascending order and which balloon they decided to color.

Decimalus Rex

Decimalus Rex is an amazing online game where children will practice comparing decimal numbers and ordering them in ascending order. Make sure there is a device for each student to play the game.

Pair students up and provide instructions for the game. Explain that each player travels back in prehistoric time with Decimalus Rex. They have to find the given decimals in the wilderness with the help of Decimalus Rex and arrange them from least to greatest.

When Decimalus Rex finds the correct decimal, he throws fire at it to arrange the decimals in ascending order. The two students in each pair play individually and compare their scores in the end. The player with the biggest score wins the game.

Rounding Decimals Online Game

This is an online game that will help students hone their skills in rounding decimals by using their knowledge of place value. To implement this activity in your class, just make sure you have enough technical devices to play the game online.

Students play this game individually, which makes it suitable for parents who are homeschooling as well. Explain to students that they will be presented with different questions where they are asked to round off a certain decimal to the nearest hundredth, thousandth, etc.

Provide a few minutes for students to complete the exercises. Then, open space for discussion and reflection. Which steps did students take to round off the given decimal? Did they use a place value chart or could they carry out the rounding without one?

Decimal Sharks Game

In this cool online game, students will strengthen their rounding competences when it comes to rounding off decimal numbers to the nearest hundredths. To implement the game in your class, make sure there is a suitable device for each student.

Homeschooling parents can also benefit from this game, as it’s an individual game. Provide instructions to students. Point out that in every round, a sentence will appear where students have to round off a given decimal number.

At the same time, sharks appear on the screen trying to reach the little goldfish. The player must find the shark that contains the correct answer and click on it to prevent it from reaching the goldfish.

However, if the player clicks on a shark that carries the wrong answer, this might have the opposite effect – the player could actually boost the ability of the shark to reach the goldfish quicker.

For each correct answer, students get points. Allow students to play as much as time allows it and then ask them to share their scores as well as their methods of rounding off the decimal numbers with others in the class.

Before You Leave…

If you enjoyed these strategies and activities for teaching decimal place value, you’ll want to check out our lesson that’s dedicated to this topic! So if you need guidance to structure your class and teach it, sign up for our emails to receive loads of free content!

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This article is based on:

Unit 2 – Place Value and Decimals