Power Up Place Value

Can the same digit be worth four, forty, or four hundred? Yes... move it through the place-value chart, and its value changes without changing the digit. Today, you will make numbers ten, one hundred, or one thousand times larger or smaller, using that simple move.

Picture columns labelled thousands, hundreds, tens, ones, tenths, and hundredths. When you multiply by ten, every digit moves one place LEFT. The digit stays the same. Its place value becomes ten times greater. Multiply by one hundred, and each digit moves two places left. Multiply by one thousand, and each digit moves three. Watch four point two seven slide two columns: four point two seven becomes four hundred and twenty-seven. Division reverses the direction. Divide by ten: move every digit one place RIGHT. Divide by one hundred: move two places right. Divide by one thousand: move three. Empty columns need zero placeholders, and the decimal point stays fixed on the chart. Do not say the digit itself is the answer. In six hundred, the six is worth six hundred because it sits in the hundreds column. After dividing by one hundred, it sits in the ones column, so the number is six.

Let's work through an example. A museum has three point six four metres of ribbon for one display. Its storeroom has one hundred times that length. How many metres of ribbon are in the storeroom? We need three point six four multiplied by one hundred. One hundred is ten times ten, so use two place-value moves. First, every digit shifts one column left. Three point six four becomes thirty-six point four. Then shift every digit one more column left. Thirty-six point four becomes three hundred and sixty-four. Check the direction: multiplying must make this positive number larger. So the storeroom contains three hundred and sixty-four metres of ribbon.

Remember: multiply by ten, one hundred, or one thousand by moving every digit left one, two, or three places; divide by moving right. Track place VALUE, and powers of ten become easy!