With a wooden ruler, you measure the length of a rectangular piec...

Question

With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (c) the perimeter of the rectangle?

Accepted Answer

Hey everybody today, we're being asked to determine the cell of the perimeters of two shapes. A regular hexagon with side lengths of 7.88 mm as well as a square table Where each side is exactly 40.2 cm. And we're supposed to use the appropriate numbers of significant figures. So remember when dealing with significant figures, when numbers are multiplied or divided, the number of significant figures in the result can be no greater. The sig figs, oops, it's red and black. The significant figures can be no greater than the factor with the fewest significant figures than the factor back there. With fewest when adding or subtracting as we're doing in this example because we're trying to find the sum the location of the decimal is what matters. Ad subtract decimal position is our deciding factor, decimal position. So this in hand let's go ahead and figure out a few things. So it would be very easy. All the answers are in millimeters. So we need to first convert all our units into millimeters as well for the hexagon, this is fine because it's already in millimeters. But for our square table it's in centimeters, this conversion however is really easy if we recall that for every one cm We have 10. So with this conversion, if we have 40.2 cm Multiplying it by the inverse of this uh conversion factor of 10 for every one cm. Our centimeters will cancel out And we'll have a final answer of millimeters. So let's go ahead and figure out our perimeters for both of these shapes. All right. The oops, alright. The hexagon in blue. So this is our hexagon. So it'll be six times 7. mm because there are six sides and each side is 7.88 mm. This will give us a final answer of 47.28 mm, 47.28 mm. Excuse me? And for the square table, which I'll write in green, our square We have four sides each 402 mm. So four times 402 mm, gives us 1608 mm. So adding these two up, Adding these two up, we get 1655. millimeters. And that is indeed our answer answer choice AA

With a wooden ruler, you measure the length of a rectangular piece of sheet metal to be 12 mm. With micrometer calipers, you measure the width of the rectangle to be 5.98 mm. Use the correct number of significant figures: What is (c) the perimeter of the rectangle?

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