Every digit in a number has a value that depends on where it sits. Move a digit one place to the left and it is worth ten times as much. That single rule is what makes it possible to write any number at all with only ten symbols.
Periods, the groups of three
Digits are grouped in threes from the right, and each group is called a period. Within every period the pattern is identical: hundreds, tens, ones. Only the period name changes.
| Period | Digits | Read as |
|---|---|---|
| Millions | 428 | four hundred twenty eight million |
| Thousands | 703 | seven hundred three thousand |
| Ones | 516 | five hundred sixteen |
Read the whole number by reading each period as a three-digit number and saying its period name: four hundred twenty eight million, seven hundred three thousand, five hundred sixteen. The ones period never gets a name spoken after it.
The value of a digit
What the 7 is worth in 4,703,516
4 7 0 3 5 1 6 ^ the 7 sits in the hundred-thousands place its value is 7 x 100,000 = 700,000
A common exam question asks for the value of a digit rather than the digit itself. The digit is 7. Its value is 700,000. Answering with the digit alone is the usual way to lose the mark.
Zeros hold the places
A zero is not nothing. In 4,703,516 the zero holds the ten-thousands place, and removing it would turn the number into 473,516, which is smaller by more than four million. When writing a number from words, work period by period and fill any missing place with a zero.
Writing six million, forty thousand, nine
millions period: 6 -> 6 thousands period: 040 -> 040 ones period: 009 -> 009 6,040,009
Common mistakes
Saying and in the middle
In United States classroom usage, the word and marks the decimal point. Four hundred and five should be read as four hundred five if you mean 405. Save the word for decimals.
Dropping a zero when writing from words
Six million, forty thousand, nine is not 6,49 or 6,040,9. Every period except the leading one must have exactly three digits.
Check yourself
What is the value of the 3 in 3,842,000?
Three million. The digit is 3 and it sits in the millions place, so its value is 3 x 1,000,000.
Write twelve million, six thousand, fifty in digits.
12,006,050. The thousands period is 006 and the ones period is 050.
Which is larger, 987,654 or 1,000,000?
One million. It has seven digits and the other has six, and for whole numbers more digits always means a larger number.
How many times larger is the 4 in 4,000 than the 4 in 400?
Ten times. Each place to the left is worth ten times the place on its right.
See also
Sources
- Place value, periods and digit value as taught in United States upper elementary mathematics. Examples on this page are our own.