Same Measure, New Unit

A ribbon marked three metres can suddenly become three hundred centimetres, without growing at all. How? The amount stays exactly the same... only the unit changes. Watch the number and unit work as a team.

First, identify the starting unit and the target unit. They must measure the same kind of thing: length with length, mass with mass, or time with time. Then find the conversion fact. One metre equals one hundred centimetres. One kilogram equals one thousand grams. One hour equals sixty minutes. Now choose the direction. Moving from a larger unit to a smaller unit makes the number bigger, so multiply by the conversion factor. Metres to centimetres means multiply by one hundred. Moving from a smaller unit to a larger unit makes the number smaller, so divide. Centimetres to metres means divide by one hundred. Keep the unit at every step, and check whether the new number should be larger or smaller. You are converting ONE stated measure. Do not multiply side lengths, and do not calculate a boundary unless the question asks for perimeter. Conversion changes the label and number, not the quantity itself.

Let's work through an example. A walking trail is three point four kilometres. How long is the trail in metres? The quantity is length, starting in kilometres and changing to metres. One kilometre equals one thousand metres. We are moving from a larger unit to a smaller unit, so the number must become bigger. Multiply three point four by one thousand. On a place-value grid, move the digits three places to the left... three point four becomes three thousand four hundred. Write the target unit: three thousand four hundred metres. Check it. A kilometre is much longer than a metre, so the number of metres should be much larger than three point four. It is. The trail has not changed length; we have renamed the same distance.

Remember: match compatible units, use the conversion fact, choose multiply or divide from the direction, then check the number's size and write the target unit. You can switch units confidently!