Lesson 4: Read and write multi-digit numbers using base ten numerals, number names, and expanded form.

Property

A number in standard form (e.g., 352,471) can be written in two other ways:

• Word Form: The number is written out using words (e.g., three hundred fifty-two thousand, four hundred seventy-one).
• Expanded Form: The number is shown as the sum of the value of each digit (e.g., $300,000 + 50,000 + 2,000 + 400 + 70 + 1$).

Examples

The number $24,583$ is written as:

• Word Form: twenty-four thousand, five hundred eighty-three
• Expanded Form: $20,000 + 4,000 + 500 + 80 + 3$

The number $709,106$ is written as:

• Word Form: seven hundred nine thousand, one hundred six
• Expanded Form: $700,000 + 9,000 + 100 + 6$

Explanation

To write a number in word form, you write out the number names for each period, separated by commas. To write a number in expanded form, you break it down into the value of each of its digits. This shows how the position of each digit determines its value. The expanded form is written as an addition sentence, summing the values of all the digits.

Property

To convert a number from word form to standard form, identify the value of each part of the name (e.g., "three hundred thousand" becomes $300,000$) and sum the values. To write it in expanded form, write the sum of the values of each digit. For example, "three hundred twenty-five" is $300 + 20 + 5$.

Examples

Given "fifty-two thousand, one hundred eight":

• Standard Form: $52,108$
• Expanded Form: $50,000 + 2,000 + 100 + 8$

Given "four hundred six thousand, seven hundred thirty":

• Standard Form: $406,730$
• Expanded Form: $400,000 + 6,000 + 700 + 30$

Given "nine hundred thousand, fifty-one":

• Standard Form: $900,051$
• Expanded Form: $900,000 + 50 + 1$

Explanation

This skill involves translating number names into their numerical representations. First, identify the place value terms like "thousand" and "hundred" to structure the number. Then, write the digits in their correct places, using zeros as placeholders for any missing values. Finally, express the number as a sum of each digit''s value to create the expanded form.

Property

To convert a number from expanded form to standard form, find the sum of all the values. The standard form is the number written using digits, and the word form is the number written out in words.

Examples

Given $400,000 + 70,000 + 5,000 + 300 + 20 + 1$:

• Standard Form: $475,321$
• Word Form: Four hundred seventy-five thousand, three hundred twenty-one

Given $80,000 + 2,000 + 600 + 9$:

• Standard Form: $82,609$
• Word Form: Eighty-two thousand, six hundred nine

Given $500,000 + 4,000 + 30$:

• Standard Form: $504,030$
• Word Form: Five hundred four thousand, thirty

Explanation

To change a number from expanded form to standard form, you add the values of each part together. This process combines the place values into a single multi-digit number. When a place value is missing in the expanded form, like the tens place in $82,609$, you must use a zero as a placeholder. Once you have the standard form, you can write the number in word form by reading each period (like thousands, ones) and writing the words you say.