Precision

# Precision - Precision Significant Figures Significant...

This preview shows pages 1–3. Sign up to view the full content.

Precision Significant Figures Significant figures are the number of digits required to express the accuracy of a particular measurement or the accuracy of a calculation involving measurements. As a general rule one assumes uncertainty in only the last digit and all other digits are considered to be certain or definite. Consider the measurement of the same solid rod using two different rulers. RULER 1 has graduations (marks) every 1/10 of a cm (i.e. every millimeter). RULER 2 has graduations every centimeter. Assume the left end of the rod and the metric rulers (not shown in the figure) are aligned perfectly. The length of the rod in centimeters is obtained by reading the rulers at the right end of the rod and estimating the last “digit”. The rulers enlarged for clarification and are not depicted to scale. That is the centimeter shown is not actually a centimeter in length. Let us examine what the reading for length would be for each ruler. Ruler 1 Ruler 2 1. Length is definitely between 4 and 5 cm. 1. Length is definitely between 4 and 5 cm. 2. Length is definitely between 4.4 and 4.5 cm. 2. Estimate length is around 4.5 cm. 3. Estimate length between 4.47 and 4.49 cm. 3. Report length as 4.5 ± 0.1 cm. 4. Report length as 4.48 ± 0.01 cm In each measurement there was but one uncertain digit-the last estimated digit. Regardless

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
RULER 1 produced the more precise measurement. The value of length utilizing RULER 1 has three “significant figures” while the value of length obtained utilizing RULER 2 has two “significant figures”. Generally for a given measurement, the value with the larger number of “significant figures” is the more precise value. Ruler 1 allows measurements to ± 0.01 cm. Consider a different rod again with the left end of both the rod and ruler perfectly aligned. If the right end of the rod is exactly over the graduation at 3.8, the length of the rod would be reported as 3.80 ± 0.01 cm. The number of significant figures is three with uncertainty found only in the last digit which is zero. This example illustrates the fact that zeros after decimal points are significant. Of course, non-zero digits are always significant in this type of measurement. Generally the numerical value of a measured quantity is reported to only one uncertain figure. The number of digits in the number is called the number of significant figures. One can assume that the non-zero digits of an experimental measurement are significant. With this assumption, rules have been devised to understand whether a zero (0) in a number is significant or not. Significant Figures in a Measurement 1. The significance of zero and non-zero digits in a number. (a) Assume non-zero digits are significant. (b) Zeros between the decimal and a non-zero digit are not significant.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern