Video: Solving Word Problems Involving Multiplication of Decimal Numbers by Powers of Ten

The height of Mount Everest, in metres, can be found by multiplying 8.848 by 1000. Find the height of Mount Everest.

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Video Transcript

The height of Mount Everest in metres can be found by multiplying 8.848 by 1000. Find the height of Mount Everest.

This is a particularly interesting problem because it’s based on a real-life fact. If we multiply 8.848 by 1000, we really will find the height of Mount Everest in metres. We know that one kilometre is the same as 1000 metres. And so, to convert kilometres into metres, do you remember? We have to multiply by 1000. And so, an interesting fact for you before we start is that this number here, 8.848, must be the height of Mount Everest in kilometres. And what this question is getting us to do, although it doesn’t tell us this, is to convert kilometres into metres.

Back to the question, we’re asked to multiply the number by 1000. What happens to a number when it’s multiplied by 1000? We know 1000 is the same as 100 times 10. Or if we say it in a different way, 10 times 10 times 10. So, multiplying any number by 1000 is the same as multiplying by 10 three times. When we multiply any number by 10, its digits shift one place to the left. Because multiplying by 1000 is 10 times 10 times 10, the digits in this number need to shift three places to the left.

First, let’s make our number out of digit cards, eight ones, eight tenths, four hundredths, and eight thousandths. Let’s start by shifting all our cards one place to the left. This is the same as if we’d multiplied by 10. Now, let’s shift them a second time. This is the same as multiplying by 10 and then by 10 again which, of course, is the same as multiplying by 100.

But to multiply by 1000, we need to shift these digits one more time. To multiply by 1000, we multiply it by 10 by 10 and then by 10 again. We shifted the digits three places to the left. By moving them three columns to the left, each digit in 8.848 is now worth 1000 times more. Although we may not have realized it until we watched the video, we’ve just converted kilometres into metres. The height of Mount Everest in metres is 8848 metres.

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