Lesson 1: Compare numbers based on meanings of the digits using >, <, or = to record the comparison.

Property

To compare two numbers, first check the number of digits. The number with more digits is greater. If they have the same number of digits, compare the digits from left to right, starting with the largest place value, until you find a place where the digits are different.

Examples

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

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.