Lesson 5: Comparing and Ordering Numbers in Various Forms

Property

To compare numbers presented in different forms (standard, expanded, word, or unit form), first convert the numbers to the same form, typically standard form. Then, compare the numbers digit by digit starting from the greatest place value.

Examples

• Compare $3,145$ and $3,000 + 40 + 5$. First, write the second number in standard form: $3,045$. Then compare: $3,145 > 3,045$.
• Compare "fifty-two thousand, six hundred ten" and $52,601$. First, write the first number in standard form: $52,610$. Then compare: $52,610 > 52,601$.
• Compare $8$ ten thousands, $4$ hundreds, $2$ ones and $80,000 + 4,000 + 20$. First, write both in standard form: $80,402$ and $84,020$. Then compare: $80,402 < 84,020$.

Explanation

Numbers can be written in different ways, such as word form, expanded form, or standard form. To compare numbers that are in different forms, it is helpful to first convert them into the same form. Converting both numbers to standard (number) form makes it easier to see the value of each digit. Once both numbers are in standard form, you can compare them place by place, starting from the leftmost digit.

Property

To order a set of numbers, compare them two at a time to determine their relative value. Arrange them sequentially from least to greatest (ascending) or greatest to least (descending).

Examples