Place value, comparing and rounding

Ten digits, endless numbers

Every whole number is written with just ten digits: \(0\) through \(9\). What makes \(3\) mean three in one number and three thousand in another is its place.

Expanded form

Zero as a placeholder

Zero holds a place open. In \(305\) it says "no tens". Leave it out and you get \(35\), a very different number.

Reading large numbers

In the US, commas separate digits into groups of three, starting from the right. Each group is read like a number from \(0\) to \(999\), followed by its name.

Comparing numbers

\(8{,}301 > 8{,}295\): the thousands match, and in the hundreds place \(3 > 2\). The symbols: \(>\) "is greater than", \(<\) "is less than". The open side faces the larger number.

Rounding

Rounding is how you estimate: \(4{,}725 + 3{,}180\) is about \(4{,}700 + 3{,}200 = 7{,}900\). If your exact answer is far from the estimate, recheck it.

Practice