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Sophie’s baby weighed 3200 grams correct to two significant figures.
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Part a) one) Write the smallest possible weight of the baby.
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The first significant figure in a number is the first nonzero digit.
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The second significant figure is the second digit after the first significant figure — that, in this case, is the two.
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The weight of Sophie’s baby has been rounded to two significant figures.
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The third digit in this number would have been the deciding digit.
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When the deciding digit is five or above, we round the number up.
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And when the deciding digit is less than five, we round down.
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To find the smallest possible weight of the baby, we need to find the lowest possible weight that would still round up to 3200 grams.
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Since the deciding digit that’s the third digit needs to be five or above, the smallest possible weight of the baby that would still round up to 3200 is 3150.
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Part two) Write the largest possible weight of the baby.
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Once again, let’s consider the third digit, the deciding digit.
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We want to find the largest possible weight that will still round down to 3200.
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For the number to still round down to 3200, this digit must be less than five.
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In fact, it’s four.
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However, 3240 is not the largest possible weight that would still round down to 3200.
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3249 grams would still round down as would 3249.9 as indeed would 3249.99.
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And we can continue this pattern.
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The number would get closer and closer to 3250; it will never quite get there.
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The largest possible weight of the baby then is 3249.99999 and so on grams.
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We could write that as 3249.9 recurring.
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Now, it’s important to differentiate between this and the upper bound of the weight.
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We say that the upper bound is 3250 grams.
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The weight could not actually be 3250 grams, but it gets so close.
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So we call that the upper limit.
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Since this is just asking us the largest possible weight, we call that 3249.9 recurring grams.
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Over the course of a month, Emily’s baby’s weight increase by seven percent.
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At the end of the month, the baby weighed 3210 grams.
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Calculate the weight of the baby at the beginning of the month.
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We cannot just subtract seven percent from the new weight of the baby.
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But there are two different ways that we can calculate the weight of the baby at the beginning of the month — that’s before the increase of seven percent.
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Let’s consider this first method.
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This method can be used in both the calculator paper and a non-calculator paper.
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Emily’s baby’s weight has increased by seven percent.
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We can say that the baby originally weighed 100 percent of its weight.
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When we increase that by seven percent, we added on and that gives us 107 percent.
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That means that 107 percent of the weight of the baby is equal to 3210 grams.
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To find the baby’s original weight or the weight at the beginning of the month, we need to calculate what 100 percent is.
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To do this, we first calculate the value of one percent.
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To get from 107 percent to one percent, we divide by 107.
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We must do the same to 3210.
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3210 divided by 107 is 30.
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So one percent of the baby’s original weight is 30 grams.
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Once we know what one percent of the weight is, we can multiply this by 100.
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One multiplied by 100 is 100 percent and 30 multiplied by 100 is 3000.
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So the baby weighed 3000 grams at the beginning of the month.
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The alternative method is to form an equation.
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Let’s call the weight of the baby at the beginning of the month 𝑥 or 𝑥 grams.
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We said since the baby’s weight had increased by seven percent, it was now worth 107 percent of the original weight.
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Percent means out of 100.
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So 107 percent is the same as 107 over 100.
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This is also equivalent to 1.07 since when we divide by 100, we move the digits to the right two places.
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So if we knew the original weight of the baby, we can multiply it by 1.07 to get the new weight.
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We don’t though; we’ve called the original weight of the baby 𝑥.
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So when we multiply 𝑥 by 1.07, we get the new weight, which we said was 3210 grams.
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To solve for 𝑥 and calculate the original weight of the baby, we can divide both sides of this equation by 1.07 and that will tell us that 𝑥 is equal to 3210 divided by 1.07, which is once again 3000.
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The baby weighed 3000 grams at the beginning of the month.