Representing Numbers in Different Ways Using Place Values (Definition, Types and Examples) – BYJUS

# Representing Numbers in Different Ways Using Place Values

It is easier to learn the meaning of numbers by relating them to objects around us. For example, the number 5 can be represented using 5 apples. But when it comes to multi-digit numbers like 55, each 5 has a different value. The difference in the value of a digit according to its place value can be demonstrated using various models....Read MoreRead Less

## Representing Numbers in Different Ways Using Place Values

When you look at different numbers, you can see that there are one-digit, two-digit, three-digit numbers, and so on. So what does this mean? Single-digit numbers have only ones. When you have enough ones to group to tens, we get two-digit numbers. Similarly, when you have tens to group as hundreds, we get three-digit numbers. If we take the number 78, 7 denotes 7 tens, and the number 8 means 8 ones. Let’s represent 78 as apples. So, as you can see, we have 70 apples and 8 apples. That is, 78 apples.

Let’s take the number 3333, for instance. The value of each digit is demonstrated below. From the extreme right, the first digit is in the ones place and it’s represented by three cubes. The next place is the tens place, where each column has 10 cubes each, which is  30 cubes. Next, in the hundreds place,  300 cubes are represented by 3 sheets where each sheet has 100 cubes. Finally, in the thousands place, there are three blocks, where each block has 1000 cubes.

Let’s take the number 345 and represent it using cubes.

Each cube represents a one. 10 ones are grouped to form a 10, which is represented in the diagram by a group of 10 cubes. Finally, 10 tens are grouped to form a hundred, which is represented as a group of 100 cubes each. So, we have 5 cubes in the ones place, 40 cubes in the tens place, and 300 cubes in the hundreds place, which gives us 345 cubes in total.

Now, if I were to take one group of cubes from the tens place and place it in the ones column, the number of cubes added to the ones place is ten. That means we now have 15 cubes in ones and 30 cubes in the tens place. The cubes in the hundreds place remain the same.

We can only shift the cube from a higher value to a lower value. We can move a cube from the tens place to the ones place, but the reverse cannot happen. For instance, a one cannot be moved to the tens place as it has not been compensated for the remaining 9 units. Only then can it be grouped to form a ten.

If we take another example, like the number 154, this is what it would look like in a place value table.

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## Questions

Represent the following three numbers by models.

1)756

2)231

1)756

2)231

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10 tens mean 10 groups of tens, which is $$10 \times 10 =100$$. Hence, 10 tens are the same as 1 hundred.