Understanding Place Value

Pre-Algebra · Axiom Academy

LESSON Understanding Place Value How a digit's position decides its value — and why each place is worth ten times the place to its right. 1. Each Place Is Ten Times the Last Our number system is built on a single rule: as you step left from one place to the next, the place is worth ten times as much. Start at the ones, multiply by 10, and you land on the tens. Do it again for hundreds, then thousands. Watch one unit leap from place to place, growing by a factor of ten on every hop. Each step left multiplies the place value by 10 2. A Digit's Value = Digit × Place Value To find what a single digit is worth inside a number, multiply the digit by the value of the place it sits in. In 3,542 , the spotlight lands on each digit in turn, lifts it out, and pairs it with its place value to compute its contribution. 3. Putting the Parts Back Together Each place contributes its own value, and the whole number is just the sum of those parts. This way of writing a number — adding up what each digit is worth — is called expanded form . Watch the four parts slide in and stack into a total. Adding the parts back together, 3 , 000 + 500 + 40 + 2 , returns the original number: 3 , 542 . Nothing is lost — expanded form and the everyday written number are two views of the same quantity.

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