Numbers to Millions: Reading, Writing, Renaming

A big number is three small numbers standing next to each other. Starting from the right, every three digits make a house: the ones house, the thousands house, the millions house. To read 4 285 306, read each house as an ordinary three-digit number and then say the house's name. Four — million. Two hundred and eighty-five — thousand. Three hundred and six. The thin gaps you see in printed numbers are exactly those house walls, which is why we write 4 285 306 and not 4285306: the gaps tell your eye where each house begins.

Zeros are the digits students drop, because they feel like nothing. But look at 30 060. The 3 is worth thirty thousand only because there are four digits after it, and two of those are zeros. Take one zero out and you get 3 060, where the 3 is worth three thousand, ten times less. The zero is doing a job: it is holding a column open so the digits to its left stay where they belong. When you write a number from words, the zeros are the part to check twice. Forty thousand and twelve is 40 012, with two zeros in the middle that the words never mention.

Renaming means reading the number in a unit that is not the ones. How many thousands are in 4 285 306? Cover everything to the right of the thousands column and read what is left: 4285. So it is 4285 thousands, with 306 left over. How many hundreds? Cover the tens and ones: 42 853 hundreds, with 6 left over. Renaming is what makes questions like 'six hundreds less than 74 251' quick. Six hundreds is 600, so the answer is 74 251 minus 600, which is 73 651 — you can see the hundreds column drop from 2 to 6 by borrowing from the thousands.

To compare two numbers, do not look at the digits at all yet. Count them. A seven-digit number is bigger than any six-digit number, so 1 002 000 beats 986 543 even though nearly all of its digits are zeros. Only when the two numbers have the same number of digits do you compare, and then you start at the left and walk right until the digits differ. 749 812 against 750 100: the first digits match, the second ones do not, and 5 beats 4, so 750 100 is larger. Everything after that point is irrelevant, however big it looks.

Populations, prices of buildings and distances in space come as millions with a decimal: 8.27 million people. That is eight whole millions plus 0.27 of a million, and 0.27 of a million is 270 thousand, so the number is 8 270 000. You can also leave it in millions and calculate there: the population grew from 8.27 million to 19.16 million, which is a difference of 10.89 million. Convert to digits only if the question wants digits. Either way, a million is a thousand thousands — six zeros — and that is the fact to hold onto.