Consider the numbers 420,350 and 470,350. We can also use the place value of the individual digits within the numbers to determine which one is less or more than the other.

For instance, let's create a table showing the place value of the numbers above:

To compare two large numbers, sometimes it is better to compare the place value of the individual digits of the numbers.

Place value refers to the value of a digit based on its position within a given number. Each digit in a number has a different place value, depending on its position (or place) from right to left.

For example, the place value of the number 3 in each of the figures in the table above is 300. This is because, when each of the numbers are written in their expanded form, the number 3 which is under the hundreds column will be multiplied by 100 in order to get its true value.

Let's expand the numbers in the table above to see the place values of the individual digits.

\(420,350\) \(=\) \((4 \times 100,000)\) \(+\) \((2 \times 10,000)\) \(+\) \(0\) \(+\) \((3 \times 100)\) \(+\) \((5 \times 10)\) \(+ \ 0\)

\(470,350\) \(=\) \((4 \times 100,000)\) \(+\) \((7 \times 10,000)\) \(+\) \(0\) \(+\) \((3 \times 100)\) \(+\) \((5 \times 10)\) \(+ \ 0\)

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Now let's see how you can compare different numbers using their place values:

1. Number of digits
When comparing 2 numbers using their place values, we first look at the number of digits within the numbers. The higher the number of digits, the bigger the number.

For example, 2,000 is bigger than 300 because 2,000 has 4 digits while the number 300 has only 3 digits.

2. The place value chart
We can also use a place value chart to compare the individual digits within whole numbers.

Each digit in a number has a different place value, depending on its position from right to left.

\(*\) The rightmost digit is in the ones place \(\Rightarrow Ones\)

\(*\) The next digit to the left is in the tens place \(\Rightarrow Tens\)

\(*\) The next digit to the left is in the hundreds place \(\Rightarrow Hundreds\)

\(*\) And so on, increasing by powers of 10 as you move to the left.

This pattern can extend to very large numbers.

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Research

Research on the internet to find all the other names of the various places on the place value chart.

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Test yourself on what you have learnt so far. Click on the link below when you are ready.

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