Video: Pack 1 • Paper 1 • Question 3

Pack 1 • Paper 1 • Question 3

03:51

Video Transcript

Calculate 3.15 multiplied by 8.9.

To multiply two decimals, it’s first much easier to imagine that there are integer values and perform the multiplication as normal. Remember it’s absolutely fine to use whichever formal written method for multiplication you prefer. The two most popular methods are the column method and the grid method.

Let’s have a look at what this process will look like using the column method. First, we’ll multiply the nine by everything in the top row. Five multiplied by nine is 45. So we put a five in the furthest column on the right and then we carry the four. One multiplied by nine is nine. And then when we add the four, we get 13. So three goes in the second column from the right and then we carry the one. Three multiplied by nine is 27. And then when we add the one, we get 28.

Next, we’re gonna multiply the eight by everything in the top row. This isn’t really an eight though. It’s actually 80. So we pop a zero in this column to show that everything is 10 times bigger. Five multiplied by eight is 40. So we put a zero in the second from right column and carry the four. One multiplied by eight is eight. And then when we add the four, we get 12. We put a two in this column and carry the one. Three multiplied by eight is 24. And then when we add the one, we get 25.

The final step here is to add these two numbers together. Five add zero is five, three add zero is three, eight add two is 10. So we put a zero in this column and carry the one. Two plus five plus one is eight and two plus zero is two. That gives us that 315 multiplied by 89 is 28035.

Let’s see what this might have looked like had we used the grid method. Eight times three is 24. So 80 times 300 is 24000. Eight multiplied by 10 is 800 and 80 multiplied by five is 400. Since nine multiplied by three is 27, nine multiplied by 300 is 2700. Nine multiplied by 10 is 90 and nine multiplied by five is 45. Finally, we add these six values together. Once again, that gives us an answer of 28035.

However, we weren’t actually being asked to calculate 315 multiplied by 89. We want the solution to 3.15 multiplied by 8.9. 3.15 is 100 times smaller than 315 and 8.9 is ten times smaller than 89. This means our answer will be 100 times smaller than another ten times. This is the same though as saying that it will be 1000 times smaller than the answer we originally calculated. To divide by 1000, we move all the digits to the right three places. That gives us an answer of 28.035.

It’s really useful to check our answer by estimating. We estimate by rounding each number to one significant figure. 3.15 rounds to three and 8.9 rounds to nine. Three multiplied by nine is 27. And you’ll notice that 27 is really close to the answer of 28.035 that we originally worked out. This can be a great way of checking whether your answer is likely to be correct. 3.15 multiplied by 8.9 is 28.035.

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