مقامی قدر
Maths · Key Stage 2 · The School
Position gives value
A digit's value depends on WHERE it sits. In 3,472 the 3 is worth three thousand, the 4 four hundred, the 7 seventy and the 2 two. The same digit 4 is worth four hundred there and four thousand in 4,213. This is why our system needs only ten digits to write any number at all, and it is the idea every other piece of arithmetic rests on.
Comparing without counting
To compare two numbers, line them up and work from the LEFT. The first place where they differ decides it, and nothing to the right can change the answer. 5,213 is bigger than 5,199 because at the hundreds place 2 beats 1 — the 99 that follows cannot rescue it. This is faster than counting and it always works.
Zero holds the place
In 407 the zero says there are no tens. Without it you would write 47, a completely different number. Zero is not nothing here — it is doing the job of keeping the 4 in the hundreds column. That is why 407, 47 and 470 are three different numbers made of almost the same digits.
Line them up and work from the LEFT. Ten thousands: 4 and 4, same. Thousands: 3 and 3, same. Hundreds: 0 and 2 — different, and 2 beats 0. So 43,270 is bigger, and nothing to the right of that column can change it, however large the digits look. Notice the 7 and the 2 in the tens column: 7 is bigger than 2, and it does not matter at all, because the hundreds column has already decided.