Cracking the Code of Place Value

The number 555 has three 5s in it — but none of them mean the same thing. The first 5 is worth 500, the second is worth 50, and the third is just plain 5. That's the secret trick behind every number you'll ever write: it's not just which digits you use, it's WHERE you put them.

- What place value means and why position changes a digit's worth - How to read and write numbers into the thousands using place value charts - How to compare numbers by looking at their highest place first - Math vocabulary: digit, place, value, standard form, expanded form

Look at 4,271. The 4 sits in the thousands place, so it's worth 4,000. The 2 sits in the hundreds place, worth 200. The 7 is in the tens place, worth 70. The 1 is in the ones place, worth 1. Add those apart values together — 4,000 + 200 + 70 + 1 — and you get 4,271 again. That's called expanded form, and it shows exactly what each digit is 'doing' inside the number.

A place value chart has columns labeled Thousands, Hundreds, Tens, and Ones. If you're told '6 hundreds, 3 tens, 8 ones, 2 thousands,' you don't write them in the order you heard them — you write them in the order of the chart: 2,638. Try building 3,905 in your head: 3 thousands, 9 hundreds, 0 tens, 5 ones. That zero in the tens place matters — leave it out and you'd get 395, a completely different number.

To compare 5,432 and 5,398, don't compare digit by digit from the left randomly — start at the highest place value. Both start with 5 thousands, so that's a tie. Move to hundreds: 4 hundreds vs 3 hundreds. 4 is bigger, so 5,432 wins, no matter what the smaller places say. This trick works for any two numbers with the same number of digits.