1.1 The place value of digits in whole numbers

Mathematics

Grade 4

Whole numbers and their relationships

Module 2

The place value of digits in whole numbers

Activity:

Recognise the place value of digits in whole numbers [LO 1.4]

Recognise and represent whole numbers in order to describe and compare them [LU 1.3]

OUR MODERN NUMBER SYSTEM: THE DECIMAL SYSTEM

• Now that we have done oral counting exercises and mental calculations, we think about the meaning of our wonderful number system.
• See what Johnny says about Susie. This sounds strange doesn’t it?

• 1+ 1 is not eleven! But look at Roman numerals: I + I = II. Then it would be correct, because II is the way the Romans wrote 2. In Activity 5 we shall learn more about Roman numerals.

1. Now let’s look at a bigger number. Just what does the number 1 111 mean, and why? Try to write down what it means:

One might say this is what it means:

2. What number do you think this diagram represents?

• Our decimal system works in groups of loose ones (units), tens, hundreds, thousands and ten thousands. We can have up to nine loose blocks. If we get one more, we say we have ten blocks/ 10 that is, one group of ten and nothing left loose. The “0” fills the empty place to say there is nothing left. With blocks, it would look like this:

• Because we cannot always draw blocks, we use the POSITION of the digits to tell us the size of the group. So we have place value:

Recap: Our Decimal Number System

In our number system we have nine symbols and “0”. We use these symbols, 1; 2; 3; 4; 5; 6; 7; 8; 9 and 0 to make any and all the numbers we need. We use the position of the digit in the number to indicate its value. So in the number 2 768 the 7 means 700 because of where it is in the number.

If there are no thousands (or digits in the other columns) we use 0 as a place holder.

Note: the 0 cannot be left out. If we left out the 0 the value of the whole number would change (e.g. 10 291 would become 1 291) so the 0 is very important.

1. Now write each of the numbers below in EXPANDED NOTATION. The one at the top of the page looks like this: 2 768 = 2 000  700  60  8

Now complete the ones below:

Note also:

When we write big numbers we leave a space between the thousands and the hundreds. This makes it easier to read the number. Key 10 403 into your calculator. Unfortunately the calculator does not leave this space. Do you see it is not so easy to read this number on the calculator when there is no space between the thousands and the hundreds? Remember to leave the space in the correct place when you are writing big numbers.

MAKING NUMBERS AND ARRANGING THEM IN ORDER

• We have seen how each digit in a number has a value, for example:

3 967 = 3 000  900  60  7.

It can be written in columns like this:

Because there are:

3 × 1 000  9 × 100  6 × 10  7

4. Now create the largest and the smallest numbers with the digits: 2; 8; 4; 1. Write them and two other numbers, still using only the digits 2; 8; 4; 1 in columns: