Place value

Requirements

I know what natural numbers are.

I know what whole numbers are.

I can write sets of numbers using the correct symbols. Can I do it?

Place value

In Grade 5, we worked with numbers of up to 6-digit whole numbers, for example 695 428.

You learned that the digits we work with (0 to 9), can be used in different places or positions in a number. Every ‘place’ has a value, such as Units, Tens, Hundreds, etc.

Study the representation where place values are indicated in the columns:

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Units

HT TT TH H T U

6 9 5 4 2 8

It represents the number 695 428.Itcanbewrittenassixhundredandninety-fivethousand four hundred and twenty-eight.

The digit 8 is in the Units column and means 8 × 1 = 8. The digit 2 is in the Tens column and means 2 × 10 = 20. The digit 4 is in the Hundreds column and means 4 × 100 = 400. And so on.

The digit 4 in the number 695 428, is in the Hundreds place. Therefore, the place value of the 4 is equal to 4 Hundreds or 4H. Thus, the value of the digit 4 is in fact not 4, but 400.

The digit 9 in the number 695 428, is in the Ten Thousands place. Therefore, the place value of the 9 is equal to 9 Ten Thousands or 9TT. Thus, the value of the digit 9 is in fact not 9, but 90 000.

What is the difference between place value and number value?

Place value is exactly what it says – the ‘place’ or position of a digit in a number. Your answer must show that you know where (in which position or place) the digit is in the number. Number value is the value of a digit in a number what value does the digit represent?

Expanded notation

We can also represent the number in three ways without the use of a table. We call these methods expanded notation (your learned this in Grade 5).

This is how we would write the number 695 428 in expanded notation:

Method 1 6 Hundred Thousands + 9 Ten Thousands + 5 Thousands + 4 Hundreds + 2 Tens + 8 Units OR 6HT + 9TT + 5TH + 4H + 2T + 8U Method 2 6 × 100 000 + 9 × 10 000 + 5 × 1 000 + 4 × 100 + 2 × 10 + 8 × 1 Method 3 600 000 + 90 000 + 5 000 + 400 + 20 + 8 = 695 428

You may abbreviate the words.

What if a number contains a 0, for example 806 043?

There is a 0 in the Hundreds place and a 0 in the Ten Thousands place.

In expanded notation it will look like this: 8HT + 0TT + 6TH + 0H + 4T + 3U

But we do not have to write 0TT and 0H in expanded notation, because you are already demonstrating that you know in which place each digit of the number must go, therefore you can write it as:

8HT + 6TH + 4T + 3U

BUT you cannot leave out the zeros when writing the number 806 043. In this number, the zeros are ‘place’ holders for Ten Thousands and Hundreds. Otherwise the number would be 8 643, which is much smaller. Can you see the difference between 806 043 and 8 643? The zeros in 806 043 are place holders for TT and H.

The digit 0 is very important in a number.

What does the 0 in 100 or in 1 000 mean? I cannot simply leave out the 0, otherwise both numbers will be just 1. The 0 is a place holder. In 100, the 0 is a place holder for Units and the other 0 for Tens.

Wow, that was a lot of information! What did we just revise?

Now you: 9 can use digits to write numbers; 9 can use words to write numbers; 9 know in which place each digit in a number is; and 9 can write numbers three ways in expanded notation.

The numbers are written in groups of three digits with a space in between each group. (This is another way in which mathematics is very precise: numbers are written in groups of three digits to make it easier to read and pronounce.)

Group 2 Group 1

Hundred Thousands

Ten Thousands Thousands Hundreds Tens Units

4 5 6 8 7 9

Let’ssaythenumber:fourhundredandfifty-sixthousandeighthundredandseventy-nine.

We divide the number into groups of three digits each, so that it is easier to read:

Group 1 The last three digits 879 are easy – eight hundred and seventy-nine.

Group 2 Thenextgroupofdigits456isfour that the group name is ‘thousand’? hundredandfifty-six thousand.Can you see

Say the number again: fourhundredandfifty-six thousand eight hundred and seventy-nine

Let’s practise saying these large numbers:

978 459 in words: nine hundred and seventy-eight thousand fourhundredandfifty-nine