Tens and Ones: Place Value, Face Value, Represent Numbers

Tens and Ones: A number system is a method to represent numbers with the help of digits or other symbols in a consistent manner. The position of a digit in a number system tells the value of that digit in the given number. For example, \(3\) in \(203\) represents \(3\) ones or \(3\), but \(3\) is \(239\) is \(3\) tens or \(30\). While the same digit is present in different numbers, the value of the digit depends on its position in that number.

The first two place values for a given number will be ones and tens, and the first three place values for a given number are ones tens hundreds. This article will cover every concept related to the placement of digits in a given \(3\) digit number at hundred’s, ten’s, and one’s place. Scroll down to know more about the ones tens hundreds of thousands of concept.

Units and Tens: Place Value of a Number

In a number, the place (local) value of a non-zero digit is the value of this digit according to its position. In Mathematics, place value refers to the position of a digit within a number. The position of each digit will be expanded when we represent the number in a general form. The positions start from a unit place, which we also call one’s position. Numerals are placed in order of place value from right to left: units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on.
Consider a two-digit number, say \(21\).

Clearly, \(21=20+1\)
\(⇒2\) is at ten’s place and \(1\) at one’s place.
In number \(21\), the place value of \(2\) is \(20\), and the place value of \(1\) is \(1\).

Thus, the place value of a digit depends upon the position it occupies in a number. The place value of the digit \(0\) is always \(0\) regardless of its place in any number.

Let us take another example.

Take a two-digit number, say \(66\)
Clearly, \(66=60+6\)
\(⇒6\) is at ten’s place and \(6\) at one’s place.

In number \(66\), the place value of \(6\) is \(60\) at tens place, and the place value of \(6\) is at the ones place.

Face Value of a Number

The face value of a digit for any place in the given number is the value of the digit itself.  For example, the face value of digit \(3\) in number \(34\) is \(3\) itself.

In \(23\), the face value of \(3\) is \(3\).

Tens and Ones

A number can have many digits, and each digit has a special place and value.

Let us understand it with the help of an example. 
Consider a two-digit number say \(87\).
The number \(87\) in expanded form can be written as \(87=80+7=8×10+7×1\).
\(⇒8\) is at ten’s place, and \(7\) is at the unit’s place.

In other words, we can say, in \(87\) the place value of \(8\) is \(80\) (\(8\) tens, i.e., \(8×10\)), and the place value of \(7\) is \(7\) (\(7\) tens, i.e., \(7×1\)).

Thus we can say that, in a two-digit number, the leftmost digit is at ten’s place, and the digit to the rightmost placed is at one’s place.

An Activity to Remember Units and Tens

To understand tens and ones better, we can use blocks, crayons, popsicles, beans or rocks. Place a pile of them on a table and show that it is easier to count them individually and in groups of ten to count the bigger numbers. So first, make groups of ten, then count the ten groups and the individual blocks separately. 

The figure given above of blocks is a rod and comprises \(10\) one’s or unit’s blocks. Thus each block represents \(1\) ten.

For example, after arranging the block in groups of tens and some with leftover blocks, we have:

We can say that “I have here four \(10\) – groups and \(4\) individual blocks.” That is four tens and four ones.

Similarly, take popsicles this time. Group them into groups of tens and some with the leftovers, if any. Count the ten groups and the ones separately.

And thus, we can say that “I have here \(1\) ten group popsicles and \(2\) leftover popsicles.” That is one tens and two ones. With this, we can learn words like ten, twenty, thirty, forty, etc.

Representation of Tens and Ones

As discussed earlier, there are many ways to represent tens and ones, but most of the time, we use the blocks. 

To represent \(1\) ten’s, we express it as,

Practice Exam Questions

To represent \(2\) ten’s, we express it as,

To represent \(3\) ten’s, we express it as,

and so on.

One’s are represented by the single blocks. For example, the number \(7\) can be represented as shown below.

To represent \(3\), we can show it as

Different Ways to Represent a Number

There are many ways to notify or represent a number. We can represent a number in base ten representation, also known as block representation of ten’s and one’s. 

The example to represent \(62\) is shown through a figure given below, making us understand the various representation of the number easier.

Tens and Ones Examples

Now, we are almost proficient in representing the number in tens and ones by the place value. Let us master ourselves by solving quite a couple of examples based on units and tens.

Example 1: Express \(47\) in the form of blocks.

Solution: We can represent \(47\) in the form of blocks as;

Example 2: Count the blocks and write the number obtained.

Solution: In the figure, there is one rod of tens and \(9\) individual blocks. So, we can write it as \(1×10+9×1=10+9=19\)

Hence, the number formed is \(19\).

Example 3: Find the face value and place the value of \(5\) in the number \(59\).

Solution: The face value of digit \(5\) is \(59\) is \(5\), whereas the place value of \(5\) is \(59\) is \(50\).

Example 4: Represent the number \(27\) in the form of blocks and rods.

Solution: We can write \(27\) as \(20+7\)
\(⇒2×10+7×1\)
We need \(2\) rods of tens and \(7\) individual blocks.
Thus, \(27\) can be represented as

Solved Examples – Tens And Ones

Q.1. A number has \(8\) tens and \(2\) ones. What is the number?
Ans: The place value of the given numbers are:
\(8\) tens \(=80\) and \(2\) ones \(=2\).
Adding these numbers together, we \(80+2=82\).
Hence, the required answer is \(82\).

Q.2. Count the tens and ones blocks and write the number.

Ans: By separating the ten’s block and one’s block, we can write it as

Hence, the number is \(23\).

Q.3. Represent \(15\) in the form of blocks.
Ans: Let us write \(15\) in the expanded form first.
\(⇒15=1×10+5\).
Thus, we have to draw \(1\) ten’s block and \(5\) single blocks.
Therefore, we can represent \(15\) in the form of blocks, as shown below;

Q.4. Form the blocks and separate them as tens and ones for each of the following given numbers.
a) \(64\)                                       b) \(73\)
Ans: First, let us express the numbers in expanded form:
a) \(64=6×10+4\)
Thus, there will be \(6\) ten-blocks and \(4\) individual blocks.
Hence, \(64\) can be represented in the form of blocks as follows:\

b) \(73=7×10+3\)
Thus, there will be \(7\) ten blocks and \(3\) individual blocks.
Hence, \(73\) can be represented in the form of blocks as follows:

Q.5. Count the number of tens and one’s blocks and write the number formed.

Answer: Here, \(4\) blocks are of tens and \(5\) blocks of ones.
Therefore, \(4×10+5=40+5=45\)
Hence, the answer is \(45\).

Summary

In this article, we discussed the position of a digit in a number that tells the value of a digit in the given number. This position of a digit can be specified in every number with the help of the place value. We learned the concept of tens and ones. In addition to this, we also learned the different ways to represent a block of tens, and lastly, with the help of examples, we made ourselves fully aware of the concept related to tens and ones.

Frequently Asked Questions About Tens and Ones

Let’s look at some of the commonly asked questions about tens and ones:

Q.1. How do you introduce ones and tens?
Ans: To introduce the concept of tens and ones, make use of blocks, crayons, popsicles, beans or rocks. Place a pile of them on a table and show that it is easier to count them individually and in groups of ten to count the bigger numbers. So first, make groups of ten, then count the ten groups and the leftover individual blocks separately.

Q.2. What is the place value of \(1\) is \(31\)?
Ans: We can write \(31\) in expanded form as \(31=3×10+1×1\).
Thus, \(3\) is at ten’s place, and \(1\) is at one’s place.
Hence, the place value of \(1\) is one’s place.

Q.3. What are tens and ones?
Ans: In a two-digit number, the value of the digit depends on its position in that number. At one’s place, the digit which is at the extreme right is known to be like one’s, whereas the digit placed at the leftmost is known to be at ten’s. For example, consider a two-digit number say \(39\).
The number \(39\) in expanded form can be written as \(39=30+9=3×10+9\).
\(⇒3\) is at ten’s place, and \(9\) is at the unit’s place.
Thus we can say, in \(87\), the place value of \(8\) is \(80\) (\(8\) tens, i.e., \(8×10\)), and the place value of \(7\) is \(7\) (\(7\) tens, i.e., \(7×1\)).

Q.4. What is the same as \(20\) ones?
Ans: \(20\) can be written as \(2×10\), which is \(2\) tens.
Thus, \(20\) ones are the same as \(2\) tens.

Q.5. How many ones make a ten?
Ans: \(10\) individual blocks of ones piled or bundled together make one ten.

We hope this detailed article on tens and ones helped you in your studies. If you have any doubts or queries regarding this topic, feel to ask us in the comment section below. Happy learning!