Video: Understanding Place Value When Multiplying and Rounding

Which of the following is closest to 5 × 103 × 60? Solve without using a calculator. [A] 30000 [B] 300000 [C] 40000 [D] 3000

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Video Transcript

Which of the following is closest to five times 103 times 60? Solve without using a calculator.

We have options 30000, 300000, 40000, or 3000. So here we’re looking at simplifying five times 103 times 60, and we’re not allowed to use a calculator. But it asks us which of the following is closest to that. So that means it would be okay to round a little bit.

So the fact that 103 is so close to 100, we will go ahead and change it to 100. So, solving this without a calculator, what looks easiest so far is five times 100. That just means we need five 100s. So 100 plus 100 plus 100 plus 100 plus 100 is equal to 500.

However, we still need to multiply 500 and 60 together. So since we can’t use a calculator, there are three zeros involved, and we’ll use that in a minute. But we can use the fact that five times six is 30. And then we need to add three more zeros. It’s a nice little trick. So we get 30000. So 30000 will be our final answer.

We also could’ve done this a little bit differently. Maybe instead we would multiply 60 and 100 together first. Well, there are three zeros, and we have a one and a six. And one times six is six, and then we add the three zeros. So now we take that number and multiply it by five. Well, we take five times six, which is 30, and then add the three zeros. And once again, we get 30000. So we would choose option A 30000.

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