What is the significant figure of a 8.37???? I know the answer is 8.4 as my teacher told me?but how did she get it ?

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The number of significant figures in your number 8.37 is 3 while the number of significant figures in 8.4 is only two. Without any of the starting numbers or operations that gave you this answer, I cannot tell you why the answer was shortened to 8.4. Here are the rules: For multiplication and division, the answer is given to the least number of significant figures of any single number in the numerator or denominator. For addition or subtraction the answer is given to the least number of decimal places of any single number in the addition or subtraction sequence. All digits from 1 to 9 are all significant digits. Place holder zeros like those in 0.002 or 200 are not significant. Each or those had only 1 SF. Trapped zeros like 2003 are significant (this number has 4 SF) and end zeros to the right of a decimal fraction like 0.100 are siginificant (this number has 3 SF) Scientific notation numbers are always supposed to be only the significant digits like 1.50 X 10^2 has 3 significant digits.