what are significant figures?

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  • 1 decade ago
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    There are several rules for determining the number of significant digits (or significant figures) in a measurement. In general significant figures are determined starting with the leftmost digit.

    All non-zero digits are significant.

    The leftmost nonzero digit is the first or most significant figure. For example, in the number 0.02340, the first significant figure is the 2.

    If there is a decimal point, the rightmost digit is the last or least significant figure. For example, in 0.02340 the first two zeros from the left are not significant but the zero after the 4 is significant.

    If there is no decimal point explicitly shown, the rightmost non-zero digit is the least significant figure. For example, in 3400 the 4 is the least significant figure since neither zero is significant in this case.

    All digits between the most significant figure and the least significant figure are significant. For example, 6.07 has three significant figures.

    The general rule of thumb in this class is that calculated results can have no more than 3 significant figures (sig figs). This usually means that results shown on a calculator must be rounded off to 3 sig figs.

    For example, 252,194,701 would be rounded to 252,000,000.

  • 1 decade ago

    Representing a number with proper significant figures is a way of representing how precisely you know a number (It is different from statistical measurements like uncertainty or standard deviation which represent uncertainty in a group of numbers). It is probably easiest to give an example, since you've already been given a definition.

    In a simple experiment, you are measuring the area of a square. You measure one side with a really great ruler and find that it is 10.89 cm. Say you lose your great ruler and measure the other side with an ordinary ruler, so you can't measure it as accurately. You determine that side is 15.5 cm long. So you calculate the area and get 168.795. The rules of significant figures say that, because your measurements aren't 100% accurate, your answer can only have the number of figures (or digits) as your least accurate measurement. 15.5 cm was the least accurate, and has 3 digits, so you answer should be rounded to 169 sq. cm to represent the accuracy to which you know the answer.

  • Kes
    Lv 7
    1 decade ago

    Significant figures refers to meaningful figures. If you measure the width of a board as 5.128 in. using calipers but measure the length as 70.5 inches, the area is 361.524 square inches but should be rounded off as 361.5 square inches because the limited accuracy of the length does not justify greater accuracy in the product of the two numbers. If you are paid $10.0523 per hour you will not get more than $10.05 in your pay check for one hour (although the computer may track the difference and pay you next time. Significance must be meaningful and that depends in part on how numbers are used.

  • Anonymous
    1 decade ago

    the more accurate term is significant digits:

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