Hundreds, Thousands, and Beyond
The distance to the Moon, the number of people in a city, the price of a house — real life is
full of big numbers, far past the tens and ones. Reading and writing them uses
the very same place-value trick, just with more columns.
Once you know place value —
that a digit's worth depends on its column — bigger numbers hold no surprises. We just keep
adding columns to the left, and each new column is worth ten times the one to its
right.
After ones and tens come
hundreds, then thousands:
1,\;10,\;100,\;1000,\;\dots
Each step multiplies by 10:
ten ones make a ten, ten tens make a hundred, and ten hundreds make a thousand. The pattern
never breaks — every time a column fills up with ten, we bundle it into one of the next column
along.
A place-value table
To read a big number we line its digits up under headings. For a four-digit number the columns
are Thousands, Hundreds, Tens and
Ones — often written short as Th, H,
T, O:
\begin{array}{|c|c|c|c|}\hline
\textbf{Th} & \textbf{H} & \textbf{T} & \textbf{O} \\\hline
3 & 4 & 5 & 2 \\\hline
\end{array}
The 3 sits in the thousands column, so it means three
thousands; the 4 means four hundreds; the
5 means five tens; and the 2
means two ones. The very same digit is worth far more on the left than on the right —
that is the whole idea of place value, stretched out wider.
Numbers get big fast. The Earth is about 12{,}742 kilometres
across — already a five-digit number. Saturn is roughly 120{,}000
km, and giant Jupiter about 140{,}000 km. You could never
count that high one by one, but place value lets you write and
read it with just our ten digits. That is its superpower.
See it laid out
Watch a number drop into a place-value table, one digit per column, then read off what each
digit is really worth. Step through it, and press Refresh for a fresh
three- or four-digit number.
Expanded form
Splitting a number into the value of each digit is called expanded form. It
is just the place-value table written out as a sum:
3452 = 3000 + 400 + 50 + 2
Two more worked examples:
-
7016 is 7 thousands, 0 hundreds, 1 ten, 6 ones:
7016 = 7000 + 0 + 10 + 6. The 0 hundreds
is what keeps the 7 in the thousands column.
-
40{,}205 is 4 ten-thousands, 0 thousands, 2 hundreds,
0 tens, 5 ones:
40{,}205 = 40000 + 200 + 5.
Reading big numbers in groups
And it never stops: ten thousands make a ten-thousand, and ten of
those make a hundred-thousand. Keep going and you reach a
million — a one followed by six zeros, 1{,}000{,}000.
Every column is still just ten times its neighbour.
Long strings of digits are hard to read, so we split them into groups of three,
counting from the right, with a comma (or a small space) between the groups:
2459013 \;\longrightarrow\; 2{,}459{,}013
The first comma marks the thousands, the second marks the
millions. So 2{,}459{,}013 reads as "two million,
four hundred fifty-nine thousand, and thirteen" — the commas tell your eye exactly where each
group begins.
Imagine a pile of coins. Bundle ten coins into a stack of ten. Stack ten of those
and you have a hundred. Stack ten hundreds — that is one thousand coins! You would
struggle to count them one at a time, but you can picture them as
1 thousand, 0 hundreds,
0 tens, 0 ones:
1000. Place value is just tidy bundling, all the way up.
Two traps to dodge
The two biggest place-value traps in bigger numbers:
-
A digit is worth its column, not its face. The
4 in 3452 is 4 hundreds =
400, not 4. Always ask which column a digit sits in before you
say what it is worth.
-
The 0 is a placeholder, not "nothing". In 305
the 0 holds the tens column empty so the
3 stays in the hundreds. Drop it and you get
35 — a completely different number. Every empty column needs its
zero.
See it explained
Sal Khan introduces the hundreds and thousands places here: