WEBVTT
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The height of a stack of paper is 3.025 centimeters.
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Given that each sheet of paper is 0.605 millimeters thick, how many sheets of paper are in the stack?
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This question is all about trying to work out how many sheets of paper there are in a stack, using only two pieces of information to help us.
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Firstly, we know the height of the whole stack of paper.
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And that’s 3.025 centimeters.
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And we’re also told the thickness of each individual sheet of paper, 0.605 millimeters.
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To find out the number of sheets of paper that fit into a stack that’s 3.025 centimeters tall, we need to use division.
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But how would we write the division that we need to work out?
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You might think that we need to divide 3.025 by 0.605.
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In other words, take the two numbers straight out of the problem.
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But it’s not quite as simple as that.
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The height of the stack of paper is given to us in centimeters.
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But the thickness of each sheet of paper is given to us in millimeters.
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To work out this division correctly, we’re going to have to convert one of the numbers so that they’re both in the same unit of measurement.
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Let’s convert our first measurement.
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That’s the height of the stack of paper and let’s change it into millimeters.
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We know there are 10 millimeters for every one centimeter.
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And so to change a measurement in centimeters into millimeters, we need to multiply it by 10.
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When any numbers are multiplied by 10, the digits move one place to the left.
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And so watch what happens when we multiply 3.025 by 10.
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The decimal place will stay where it is.
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And see what happens to the digits.
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They’ve shifted one place to the left.
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Now both measurements are in millimeters.
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We can think about dividing.
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We need to find the number of 0.605s that there are in 30.25.
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This seems like quite a tricky division to have to work out.
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Both numbers are decimals.
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Is there a way that we could change both numbers and turn them into integers or whole numbers?
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We’ve already said that the digits in a number move one place to the left when they’re multiplied by 10.
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What if we multiply 0.605 by 10 three times, or in other words, multiply it by 1000?
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Then, the digits will move three places to the left.
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One, that’s the same as multiplying by 10.
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Two, that’s the same as multiplying by 100.
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Three, that’s the same now as multiplying by 1000.
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We’ve turned our decimal into a whole number.
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So we can change our divisor to 605.
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But we now need to make sure that the answer to our division stays the same.
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So because we’ve multiplied the divisor by 1000, we’re going to have to do the same to 30.25.
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So we start with 30.25.
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Multiplying by 10 causes the digits to shift one place to the left.
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Now we’ve multiplied by 100 which gives us a whole number.
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But we need to carry on because we need to multiply by 1000 to keep the division the same, so one more shift to the left, 30250.
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By multiplying both numbers by 1000, we’ve managed to turn them both into whole numbers without changing the answer to the division.
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Now we can get on to find the answer.
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We can’t work out how many 605s there are in three or 30 or even 302.
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So we need to consider the first four digits of our number.
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How many 605s are there in 3025?
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Again, this might seem tricky.
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We don’t know our 605 times table.
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But as usual, there’s often a method that we can use or a strategy to help.
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In this case, we can use estimation to help.
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3025 is very close to 3000.
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So let’s round it down to 3000.
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And 605 is also very close to 600.
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So we can round both numbers down.
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Can you see a factor in there that we can use to help us?
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We know that 30 divided by six equals five.
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This means 300 divided by 60 is also five.
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And this means we know that 3000 divided by 600 is five too.
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So our estimate for 3025 divided by 605 is five.
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Let’s multiply 605 by five to see how close we get to 3025.
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Again, we can make things easier for ourselves here.
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We know that 605 multiplied by 10 is 6050.
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So 605 multiplied by five, which is half of 10, will give us an answer that’s half of 6050.
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Half of 6000 is 3000.
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Half of 50 is 25, 3025.
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The number of 605s in 3025 is five exactly.
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What we do at this point normally with long division is to subtract to show there’s no remainder.
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3025 take away 3025 is zero.
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And we’d also bring down the last digit to divide, but that’s a zero to.
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So the number of 605s in zero is zero.
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This has been quite a tricky question to answer and there are a lot of steps involved.
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We had to convert our measurements so that they were same units.
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And finally, we had to use some facts we knew already to help us divide the numbers that we created.
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Even though a question could look tricky, there’s often a strategy or a fact you know already that you can use to help.
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The number of sheets of paper that there are in the whole stack is 50.