# Measurements statistics and significant digits All measurements contain some amount of uncertainty. For example, if you use a standard ruler to measure the length of a stick, you may measure it to be In scientific notation, all reported digits are significant. Their main purpose is to address the pervasive problem of reporting too many digits.

### Round each measurement to three significant figures

This reflects the fact that the significance of the error is the same in both cases, relative to the size of the quantity being measured. This is done because greater precision is immaterial, and usually it is not possible to settle a debt of less than the smallest currency unit. For example, has three significant figures and hence indicates that the number is precise to the nearest ten. This also allows specifying a precision in-between powers of ten. You suspect the child has a fever, so you check his or her temperature with a thermometer. The rule of four gives three decimal places for risk ratios from 0. Many mechanical balances, such as double-pan balances, have been replaced by digital scales, which can typically measure the mass of an object more precisely. If the measurements going into the calculation have small uncertainties a few percent or less , then the method of adding percents can be used for multiplication or division.

In this instance a combination of significant digits and decimal places, the rule of four, 11 works best: round the risk ratio to two significant digits if the leading non-zero digit is four or more, otherwise round to three.

However, in Figure 4, the GPS measurements are concentrated quite closely to one another, but they are far away from the target location. Zeros appearing anywhere between two non-zero digits are significant: Check Your Understanding Determine the number of significant figures in the following measurements: 0.

The smallest unit or fraction of a unit you can read should give you an idea what the precision of your measurement is. The number 0. Whereas a mechanical balance may only read the mass of an object to the nearest tenth of a gram, many digital scales can measure the mass of an object up to the nearest thousandth of a gram. Key Takeaways Significant figures properly report the number of measured and estimated digits in a measurement.

### Importance of significant figures

Figure 3. Reporting it rounded to two significant digits, as 23 7. All nonzero digits are significant; zeros between nonzero digits are significant; zeros at the end of a nondecimal number or the beginning of a decimal number are not significant; zeros at the end of a decimal number are significant. If all else fails, the level of rounding can be specified explicitly. Calculate the percent uncertainty of a measurement. So could have two, three, or four significant figures. The zeros in What are the major or minor units on the scale? A double-pan mechanical balance is used to compare different masses. A decimal point may be placed after the number; for example "
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