It is important to note that trailing zeros to the left of a decimal point, but to the right of the first non-zero figure (like the bolded red zeros in 78 000) are always considered insignificant. In this case as well, there are still only three significant figures: the zero is a placeholder. Likewise, we could discuss the length of the leaf in meters: the leaf is 0.0352 m long. It is also 35200 micrometers (mm) long – but even if we use mm to discuss the measurement, there are still only three significant figures, since the last non-zero number indicates the first estimated, or uncertain position. For example, in the example used above, the leaf is 35.2 mm long. In some instances, you might only be able to measure a value to the nearest hundred or thousand – or even a larger number! In this case, zeros are used as placeholders for significant digits. Likewise, if you read that someone else has found a leaf that measures 4.568 cm, you can assume that this person measured with a ruler that had markings every hundredth of a cm and estimated the final digit (the 8 in 4.568). If you were to make your own measurements, your significant digits should include all of the measurable digits (the digits that correspond to the marks on the ruler) as well as one estimated position beyond the smallest measureable digit (the 5 in 3.5 cm, and the 2 in 3.52 cm). These are called significant digits or significant figures. In this way, the number of digits in the measured value gives us an idea of the maximum accuracy of the measurement. Using the second ruler, it’s possible to estimate that the leaf is 3.52cm long, but it is not possible to measure that accurately with the first ruler. Because it’s closer to the 3.5 marking, you might estimate that the leaf is 3.52 cm (or 35.2 mm) long. On the other hand, if you measured the same leaf with a ruler that had markings every millimeter (mm), as drawn below, you can see that the end of the leaf actually falls between the markings for 3.5 and 3.6 cm (or 35 and 36 mm). In this example, illustrated below, the leaf is longer than 3 cm and shorter than 4 cm, so you might estimate that the leaf is 3.5 cm long. For example, you could measure the length of a leaf with a ruler that had markings every centimeter (cm). When discussing mathematical measurements in science, it is important to understand that the way a measurement is taken affects its accuracy. Life Sciences Cyberbridge Significant Figures
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