Reading and Writing Large Numbers

Large numbers are grouped in threes, separated by commas. Each group is a period.

Period is a group of three digits in a large number, like the thousands period.

Read one period at a time

342,715 reads as "three hundred forty-two thousand, seven hundred fifteen".

Expanded form

342,715 is 300,000 + 40,000 + 2,000 + 700 + 10 + 5.

Zeros still hold places

In 40,006 the zeros keep the 4 and the 6 in their proper places.

Numbers are read in groups of three

The commas in 348,275 split the number into periods: 348 thousands and 275 ones. Read each group as an ordinary three-digit number and say the period name after it: "three hundred forty-eight thousand, two hundred seventy-five". The commas are a reading aid, nothing more.

Writing from words

To write "sixty thousand, four hundred five", build it period by period: 60 in the thousands period, 405 in the ones. That gives 60,405. The zeros are essential — they hold the empty places open, and leaving one out shifts every digit to its left.

Expanded form for large numbers

348,275 is 300,000 + 40,000 + 8,000 + 200 + 70 + 5. Writing it out this way makes each digit's value explicit, and it is exactly the decomposition that column addition relies on. Expanded form is not busywork; it is the algorithm written honestly.

A note on the word "and"

In careful mathematical reading, "and" marks the decimal point, so 405 is "four hundred five", not "four hundred and five". Everyday speech uses "and" freely and no one will misunderstand you. Knowing the convention matters most when decimals arrive.