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 (a) the area of the rectangle?

Accepted Answer

Hey everyone today, we're dealing with the problem about significant figures. So we're told that using a vernier caliper, we've measured a rectangular cardboard to have a length. Let's write this down. It has a length of 17.32 cm And it has a width of 12 cm was 12. cm. What these values were being asked to find the area of this cardboard box. Of this rectangular cardboard box using appropriate significant figures. So before we get to actually multiplying and finding the area, we need to understand some rules for significant figures. So when it comes to multiplication, multiplication and let me write this in blue. When it comes to multiplication, multiplication or division, let me amend that. Multiplication or division. The number of sig figs that we can have a number of significant figures that we are allowed to have can be no greater. It has to be less than or equal to or it should be equal to rather the factor with the fewest significant figures. So factor with fewest sick fix and for addition or subtraction, which will let me right then read for an ad for addition or subtraction. It only depends on the decimal point. Sigfig depends on the position of the decimal point, I should say depends on decimal position. So since we're dealing with area we have to multiply the length and the width to get the rectangular cardboard boxes area or rectangular cardboard. Sorry, it's not a box. That volume. So we'd have to multiply linked by with because as we can recall area of a rectangle is simply length times with. So if we multiply it we can multiply it out very easily. It's just 17.32 centimeters. Multiplied by 12.0 centimeters. Which gives us a value of 207. centimeters squared. However, again recall our rules at the top. The number of significant figures we have in our answer should be equal to the or should be equal to the factor that has the fewest significant figures. So between our length and our width. While the length has 12 sorry, 1234 significant figures. While the width has 12 and three, the zero is indeed a significant figure. So since there are three significant figures in the with and four in the length, three is less than four. So we have to use three significant figures as shown in the with So three significant figures here would be 1, 2 and three. So our final answer with the proper number of significant figures will therefore be 207 cm squared. Or sorry, not 207. My bad. We have to round up Because the in the 10ths place It is eight which will round up to 208. My bet. So our answer will be 208 cm squared or ants. Choice be I hope this helps. And I look forward to seeing you all in the next one

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