A.5 Convert numbers between words and digits

Digits are the symbols we use to write numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. When we put digits together, we form numbers like 3,425. Number words are the words we use to say or write those numbers, such as "three thousand four hundred twenty-five."

Understanding how to move between digits and words is an essential math skill. It helps us read prices, understand distances, write checks, and communicate clearly about large amounts.

To correctly convert between digits and words, you must understand place value. Each digit in a number has a value based on its position. From right to left, the places are: ones, tens, hundreds, thousands, ten thousands, hundred thousands, and millions.

For example, in the number 4,628,395 (four million six hundred twenty-eight thousand three hundred ninety-five), each group of three digits is called a period: the millions period, the thousands period, and the ones period.

Follow these steps to change a number written with digits into number words:

1. Identify the periods. Place commas to separate the digits into groups of three from the right. For instance, write 52370 as 52,370.
2. Read each period separately. Start from the left. Read the three-digit number in the period, then say the period name (thousand, million), but do not say "ones" for the last period.
3. Connect with correct hyphenation. Within each period, if the last two digits are 21 through 99 (except tens like 30, 40), use a hyphen: twenty-one, ninety-nine.
4. Include zeros correctly. If a period is all zeros, skip it. For example, 8,000,301 is "eight million three hundred one" (the thousands period is zero).

Going from words to digits is like building a number. Use this method:

1. Spot the period words. Look for the words "thousand" and "million." They tell you where a new group starts.
2. Write digits for each group. Translate the words before "thousand" into a 3-digit number. Then translate the words before "million" into a 3-digit number. Finally, write the last group (ones) as a 3-digit number.
3. Fill with zeros. If a group has fewer than three digits, add zeros in front to make it three digits (except for the millions group if it's the first).
4. Remove the commas and combine. String the digits together. Then place commas to check your work.

Some conversions are more challenging because of zeros or unusual word forms. Keep these rules in mind:

• Zero in a period: If a period is zero, you do not say it at all. For example, 9,000,002 is "nine million two." (The thousands period is silent.)
• Internal zeros: In a period like 301, you say "three hundred one." You do not say "three hundred zero one" or "three hundred and one."
• Hyphens: Always hyphenate numbers from twenty-one to ninety-nine when they are part of a larger number. Example: 1,245 = one thousand two hundred forty-five.
• Teen numbers: Be careful with 12–19. They are unique words: twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen.

Even a brilliant student who understands place value can make small errors. Watch out for these frequent pitfalls:

• Forgetting commas or misplacing them. Use commas to separate periods. The number 12456 is confusing; write it as 12,456 to see it's twelve thousand four hundred fifty-six.
• Missing zeros as placeholders. For "eight thousand nine," students sometimes write 89 or 8,09. The correct digits are 8,009. The thousands period is 8, and we need two zeros to hold the hundreds and tens places before the 9 ones.
• Hyphen errors. Writing "twenty four" instead of "twenty-four." Always hyphenate 21–99 when they are the last two digits of a number.
• Mixing up tens and teens. "Seventy" vs. "seventeen." Double-check the ending.

Study these additional examples. They cover a range of situations, including numbers with many zeros and numbers with all periods filled.

Now practice translating words into digits. These examples gradually increase in difficulty.

Being able to switch between number words and digits is not just a classroom exercise. We use in real life also, for example, we use it when:

• Writing a check: You must write the amount in words and digits.
• Reading large numbers: News articles mention millions of dollars or thousands of people.
• Filling out forms: Some official documents ask for numbers in words to avoid errors.
• Telling temperatures or distances: "The trail is two thousand four hundred miles long" helps you picture the distance.

Here is a quick summary of everything covered. Use this as a checklist when you do your work.

• Rule 1: Identify periods (millions, thousands, ones) using commas in digits or the words "million" and "thousand" in word form.
• Rule 2: Within each period, read or write the hundreds, then tens and ones. Use hyphens for 21–99.
• Rule 3: Never say "and" when writing whole numbers.
• Rule 4: If a period is zero, skip it entirely.
• Rule 5: When going from words to digits, every period after the first must have exactly three digits—add leading zeros if necessary.
• Rule 6: Use commas in digit form to make the number easier to read and to check your work.