Reading and Writing Digits

Every number is built from digits, and every digit's job depends on where it sits inside the number. Reading and writing digits is the skill of turning a number written with digits, like \(3{,}482{,}691\), into words, and turning a number written in words back into digits. To do this well, you need a solid sense of place value, since the position of each digit tells you whether it is worth ones, tens, hundreds, thousands, or more.

Before working through this lesson, it helps to be comfortable with identifying the place value of a digit, since reading a number correctly starts with knowing what each digit represents.

Large numbers are easier to read when you split them into groups of three digits, starting from the right. Each group is called a period, and periods are separated by commas. The first period on the right is the ones period, the next is the thousands period, and after that comes the millions period.

Reading a number is simply reading each period from left to right and saying its name after it, except for the ones period, which has no extra name. Writing the number in words uses the exact same grouping in reverse: you build the words period by period, then join them together.

If you want extra practice organizing digits before you read them, the lesson on place value tables of multi-digits shows how to lay a number out clearly by column.

To read a number such as \(3{,}482{,}691\), work through it period by period:

• Millions period: 3 becomes "three million"
• Thousands period: 482 becomes "four hundred eighty-two thousand"
• Ones period: 691 becomes "six hundred ninety-one"

Put together, the number reads as "three million, four hundred eighty-two thousand, six hundred ninety-one." Notice that the word "and" is not used between periods in standard number reading. "And" is reserved for the decimal point, as in "twelve and five tenths" for \(12.5\).

Writing numbers in words follows the same period-by-period approach, just written out fully.

Example 1: Write \(2{,}506\) in words.

Since there is no hundreds digit worth mentioning beyond the thousands, break it into 2 thousands and 506 ones: "two thousand, five hundred six." You can check this against the digits themselves: \(2{,}506 = 2\times1000 + 5\times100 + 0\times10 + 6\times1\).

Example 2: Write \(50{,}032\) in words.

The thousands period is 50, giving "fifty thousand," and the ones period is 032, giving "thirty-two." Notice the zero in the hundreds place is not spoken, since a zero digit contributes nothing to the words. The full answer is "fifty thousand, thirty-two."

Understanding how each digit's expanded form breaks apart a number can make these word problems easier to check, since expanded form shows exactly what each digit is worth before you translate it into words.

Going the other direction, you start from the words and rebuild each period.

Example 3: Write "seven hundred fourteen thousand, sixty" in digits.

"Seven hundred fourteen thousand" fills the thousands period with 714, and "sixty" fills the ones period with 060. Combining these periods gives \(714{,}060\).

A common error here is forgetting to hold a place with a zero. Since "sixty" has no hundreds digit, that spot in the ones period must still be filled with a 0, otherwise the value of the number changes completely.

• Adding the word "and" between periods, such as writing "three hundred and forty-five," when standard number reading skips it
• Dropping a zero placeholder digit, which shifts every remaining digit into the wrong place value
• Misreading the boundary between periods, especially between thousands and millions in longer numbers

Practicing with a variety of numbers, and double checking your answer by breaking the number apart again, is the most reliable way to avoid these slips.

Related lessons

• Math 3