Estimations digit

The measurements reported in (a) and (c ) cun easily be seen to have two decimal places. Since they arc reported to the nearest hundredth of a centimeter, they must have been made by the more accurate ruler, the millimeter ruler. The measurements reported in (/ ) and id) were made with the centimeter ruler at the fop. In part (e). the 0 at the end shows that this measurement was made with the more accurate ruler. Here the distance was measured as more nearly 4.40 cm than 4.41 or 4.39 cm. Thus, the results are estimated to the nearest hundredth of a centimeter, but that value just happens to have a 0 as the estimated digit. 

Underline the estimated (farthest right) digit in each value. This is a technique you can use to help you keep track of the number of estimated digits in your final answer. 

Significant figure — A convention for recording quantitative data in which all the certain, or actually read, digits plus the first uncertain, or estimated, digit are used to write the resulting number of a measurement [i]. 

In the answers to addition and subtraction problems, the estimated digit that is farthest to the left is the last digit that can be retained. For example, let s add... 

The leftmost estimated digit is the last digit that can be retained in the answer. 

The estimated digit must be read between the millimeter markings on the top ruler. Why is the bottom ruler less precise ... 

When you take measurements in your chemistry laboratory, record every digit that each instrument allows, and include one additional estimation digit. This is very important, as you will see in the next lesson, because when you perform calculations with these measured values, our answers can only be as accurate as our least accurate measurement. Before you use an instrument for a measurement, you should look at it and determine to what place value it will allow you to measure. Look at the ruler section shown here in Figure 2-3 a. 

Upon examination, you should note that each line or gradation on the ruler represents a tenth of a centimeter. This means that you can accurately measure the length of an object to the tenth of a centimeter. In science, remember, you are allowed to add one additional estimation digit. This means that you can add a digit, which estimates how far between lines an object appears to reach. The place value that you should record to is dictated by the instrument, not the object that you are measuring, and every student who uses this ruler should be recording his or her measurements to the hundredth of a centimeter. 

An estimation digit is added to certain digits of each measurement in order to report the measurement with maximum precision.]... 

In general, though, unless you are told to do otherwise, the conventional practice in using instruments such as a graduated cylinder is to report all of your certain digits and one estimated digit. For example, if you were asked to measure the volumes shown in Figures 1.13 and 1.14, you would report 8.74 mL and 8.00 mL unless you were told to report your answer to the tenth place. 

Figure 2.12 The markings on the ruler represent known digits. The reported measurement includes the known digits plus the estimated digit. The measurement is 5.23 cm. 

Infer What is the estimated digit if the iength of an object being measured faiis exactiy on the 5-cm mark ... 

State how a measured value is reported in terms of known and estimated digits. 

The significant figures include all those known with certainty plus one estimated digit. 

---