You can already read numbers in the thousands, and you know each place is ten times the next. Big numbers up to a million use the same places, grouped in threes.
Idea clave
Commas split a number into periods of three digits: the ones period (hundreds, tens, ones) and the thousands period (hundred thousands, ten thousands, thousands). Read the thousands period, say "thousand", then read the last three digits.
Por qué funciona
Each period has the same three places: hundreds, tens and ones. The thousands period counts thousands the same way the ones period counts ones. So $305{,}062$ is "three hundred five thousand" and "sixty-two." The comma is where you say "thousand."
Ejemplo resuelto: Words to digits
Write forty thousand six in digits.
- "Forty thousand": the thousands period is 40, so write $40$, then a comma.
- "Six": the ones period must have exactly three digits: hundreds 0, tens 0, ones 6, so $006$.
- Put them together: $40{,}006$.
Respuesta: $40{,}006$
Ejemplo resuelto: Expanded form
Write $305{,}062$ in expanded form.
- Read each nonzero digit with its place value: 3 hundred thousands, 5 thousands, 6 tens, 2 ones.
- Zeros add nothing, so leave them out of the sum.
Respuesta: $300{,}000 + 5{,}000 + 60 + 2$
Error común
Writing "forty thousand six" as $4{,}006$ (a zero dropped) or $400{,}006$ (a zero added). Every period after the first needs exactly three digits, so fill empty places with zeros. Check by reading your number back aloud.