Transcript

INSTRUCTOR:

Since we use a number system in base 10, special things happen when you multiply or divide by powers of 10. A place value table is useful for explaining what happens. To work out the effect of the calculation 123.45 times 10, move each digit one place to the left, which makes every digit 10 times bigger to give us 1,234.5.

Note that the decimal point is not moving one place to the right. Thinking like this is the instrumental way of thinking about it, are you using rules without reasons? The digits all move one place to the left to become 10 times as big. That is the conceptual way of thinking about it, or how the maths works.

Multiply 23.45 by 100 by moving each digit two places to the left to get 2,345. we do not need to show the decimal point if there are no digits afterwards. So we write 2,345. 3.04 divided by 100 can be found by moving each digit two places to the right to make them 100th the size they were before. We need to add a 0 in the tenths place as a place holder for neatness a 0 in the units place. 3.04 divided by 100 equals 0.034.

What happens to the rule which tells you that to multiply by 10, you must add a 0? 2.4 times 10 equals 24. As we can see, each digit moves one place to the left. So simply adding a 0 on the end does not work with decimal numbers.

However, we know that this method holds for whole numbers. 24 times 10 equals 240. Let's look at the place value diagram. Two 10's plus 4 units is multiplied by 10. Move each digit one place to the left to give us 200 plus four 10's. We need to add a 0 as a place holder in the units column. That is why it works to 0 on the end of a whole number when multiplying by 10.