Why do you use multiplication to change a larger unit to a smaller unit?

Answer 1

When you change from a larger unit to a smaller unit there will be more of them; thus you multiply.

eg millimetres are smaller than centimetres. Thus it requires many more of them to measure the same distance. Thus when converting metres to millimetres a multiplication will be required.

If you draw a line 3.5 cm long with your rule, and then measure it in mm you will find that it takes 35 mm. If you look closely you will see than 1 cm = 10mm, thus 3.5 cm = 3.5 × 10 mm = 35 mm.

Answer 2

In addition to the other answer you got: Actually, you can multiply or divide - depending on the conversion factor provided. Let's say you want to convert from meters to millimeters. Since 1 m = 1000 mm, you MULTIPLY by 1000. However, if you look at the statement that 1 mm = 0.001 meters, you need to DIVIDE by 0.001 to convert - obviously with the same result.A good way to visualize the conversion is to multiply by a fraction which contains the same measurement in the top and bottom (multiply by 1). For example, since 1 m = 1000 mm, the fraction 1 m / 1000 mm is equal to one. So is the fraction 1000 mm / 1 m. Now, if you want to convert 5 m to mm, you multiply it by 1000 mm / 1 m - and since you are multiplying by 1, you won't change the result. The original units cancel, and you are left with mm.