1.6 MEASUREMENT: SIGNIFICANT DIGITS AND ACCURACY1.7 MEASUREMENT: PRECISION

Objective:•Differentiate between accuracy and precision.

Exact number – a number that has been determined as a result of counting. The main emphasis of mathematics.

Approximate numbers – inexact number resulting for the measurement process. Usually how most technical data are

collected Better the measurement device, the

better the measurement.

The accuracy of a measurement refers to the number of significant digits.

Significant digits – the number of units we are reasonably sure of counting. They include all the known digits

recorded from an instrument plus one estimated digit.

The greater the number of significant digits, the greater the accuracy.

Determining Significant Digits1. All non-zeros are significant

156.4 m has four significant digits (measurement indicates 1564 tenths of meters)

2. All zeros between significant digits306.02 km has five significant digits (measurement indicates 30602 hundredths of kilometers)

3. In a number greater than 1, a zero that is specifically tagged, such as by a bar above it, is significant

2304 000 km has three significant digits (measurement indicates 2304 thousands of kilometers)

4. All zeros to the right of a significant digit and a decimal point are significant.

86.10 cm has four significant digits (measurement indicates 86104 hundredths of centimeters)

5. In whole-number measurements, zeros at the right that are not tagged are not significant.

2500 m has two significant digits (25 hundreds of meters)

6. In measurements less than 1, zeros at the left are not significant.

0.00752 m has three significant digits (752 hundred-thousandths of a meter)

Scientific notation The first factor indicates the number of

significant digits.

Precision – refers to the smallest unit with which a measurement is made, that is, the position of the last sig. fig. 385 000 km has a precision of 1000 km 0.025 g has a precision of 0.001 g 0.0500 s has a precision of 0.0001 s 12.3 m has a precision of 0.1 m