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Significant figures

Numerals are often expressed as approximate values The concept of significant figures (or significant digits) is an assessment of the accuracy of the numeral as an expression of the real value of the number that it represents. When a number is given in decimal notation, the error should not exceed a half unit of the last digit retained. Suppose a number has been rounded to 1400. We should be able to expect that before it was rounded to the nearest whole number it was greater than or equal to 1399.5 and less than 1400.5 Hence it should be no more than 0.5 different due to the rounding. Hence we can say that the four figures are reliable, and that the number has been expressed to four significant figures.
However, suppose we had been rounding to the nearest 100, which we might do in scientific or other practical situations. Then 1379 would also be written as 1400 but only the first two digits would be significant. Then we would know that the true value was greater than or equal to 1350 and less than 1449.
When numerals are written in standard form, it is easy to see how many significant figures they have. In the examples above, the first example of 1400 which was to four significant figures should be written as 1.400 x 103, while the second example of 1400 which was to two significant figures should be written as 1.4 x 103.
The numeral 2.57000 x 102 is intended to indicate that it has six significant figures.
Similarly 0.000378 can be written as 3.78 x 10-4 and has three significant figures.

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