Ordering Numbers and Place Values

Understanding Ordering and Place Values

The place value of a digit in a number refers to the value it holds depending on its position within the number.
For example, in the number 345, the digit ‘3’ is in the hundreds place, ‘4’ is in the tens place, and ‘5’ is in the units place.
Ascending order is when numbers are arranged from the smallest to the largest.
Descending order is when numbers are arranged from the largest to the smallest.

Comparing numbers comes down to looking at each place value, starting from the largest.
For instance, to compare 456 and 465, start at the hundreds place. Both numbers have ‘4’ here, so move to the tens place. We see ‘5’ and ‘6’, hence 456 is smaller because ‘5’ is smaller than ‘6’.
To arrange multiple numbers in ascending order, find the smallest number first and place it at the beginning. Repeat this process until the numbers increase throughout the sequence.
For descending order, find the largest number first and place it at the start of the sequence, ensuring the numbers decrease throughout.

Problem: Arrange the numbers 456, 465, 645 in ascending order.
- Solution: 456, 465, 645
Problem: Arrange the numbers 1234, 1324, 1243 in descending order.
- Solution: 1324, 1243, 1234
Problem: What is the place value of ‘5’ in the number 6543?
- Solution: The ‘5’ is in the hundreds place.

Ensure that you are comfortable with multiples of 10 (tens, hundreds, thousands etc), as this will determine the place values.
Always double check your comparisons and the orders you have arranged your numbers in.
When it doubt, writing the numbers out in expanded form (e.g. 400 + 50 + 6 for 456) can help clarify the place values.