Comparing and Ordering Numbers

Key Concepts

In Grade 3, we learn how to compare and order numbers. This involves understanding the value of each digit in a number and using symbols like <, >, and = to show relationships between numbers.

Comparing Numbers

When comparing two numbers, we look at their values. The number with more digits is always greater. For example, 123 is greater than 45 because 123 has three digits and 45 has only two digits.

If two numbers have the same number of digits, we compare the digits starting from the leftmost (most significant) digit. For example, to compare 345 and 367, we first look at the hundreds place. Both have 3 in the hundreds place, so we move to the tens place. Since 4 is less than 6, 345 is less than 367.

Ordering Numbers

Ordering numbers means arranging them in a sequence, either from smallest to largest (ascending order) or largest to smallest (descending order). To order numbers, we first compare them and then arrange them accordingly.

For example, to order the numbers 12, 45, 32, and 8 in ascending order, we first compare them: 8 is the smallest, followed by 12, then 32, and finally 45. So, the ascending order is 8, 12, 32, 45.

Examples

Let's compare the numbers 56 and 78. Since 56 has fewer digits than 78, 56 is less than 78. We write this as 56 < 78.

Now, let's order the numbers 23, 15, 40, and 10 in descending order. We compare them: 40 is the largest, followed by 23, then 15, and finally 10. So, the descending order is 40, 23, 15, 10.

Analogies

Think of comparing numbers like comparing the height of buildings. A skyscraper with 100 floors is taller than a house with 2 floors. Similarly, a number with more digits is greater than a number with fewer digits.

Ordering numbers can be likened to arranging toys by size. You would place the smallest toy first and the largest toy last when arranging them in ascending order.