Sig Figs Multiplication And Division

Multiplication and Partitioning

Now that we can identify significant figures, we can consider the rules for pregnant figures in calculations. When multiplying two numbers, the important value is the number of meaning figures. If the numbers being multiplied have 3 pregnant figures, and so the product will accept three significant figures. For example, if y'all wanted to detect the surface area of a rectangular yard, you would measure the length and width. If the length was Fifty = 3.two meters, and the width was W = 2.8 meters, then the expanse would be A = Fifty x W = (iii.ii thousand)(2.viii m) = 8.96 thou². But since the length and width simply have ii significant figures, the area will only have two significant figures. You therefore written report the area every bit A = nine.0 m².

When the two factors being multiplied don't have the aforementioned number of significant digits, the product volition take the smaller of the 2 numbers of sig-digs. If the width of your yard was v.2 meters and the length was xiii.5 meters, yous would still only report the surface area with ii meaning figures: A = 7.0 10 10ⁱ m². This is an case of a more general rule for significant figures:

The uncertainty in a calculated value is determined by the uncertainty of the least sure original number.

Division is simply the inverse of multiplication, so the pregnant figures for a quotient will exist determined in the same way as the pregnant figures of a product. We can summarize the rule for division and multiplication as

When multiplying or dividing two or more numbers, count the pregnant figures in each of the original numbers. Take the smallest of the numbers of significant figures. The product or quotient will accept that minimum number of significant figures.