Student A measures an object and records a value of 1.5 cm. Student B measures the same object and records a value of 1.50 cm. They have both done their measurements correctly. Why do these measurements differ

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Student A measures an object and records a value of 1.5 cm. Student B measures the same object and records a value of 1.50 cm. They have both done their measurements correctly. Why do these measurements differ?
### Measurement Accuracy and Precision

In this example, we examine the measurements taken by two students to understand the concepts of accuracy and precision in measurement:

**Problem Statement:**

1. **Scenario:**
   - Student A measures an object and records a value of 1.5 cm.
   - Student B measures the same object and records a value of 1.50 cm.
   
   Both students have performed their measurements correctly. Why do these measurements differ?

**Multiple Choice Answers:**
   
   a. They aren't different.
   
   b. Person A used a ruler with markings every 0.1 cm. Person B used a ruler with markings every 0.01 cm.
   
   c. Person A used a ruler with markings every 1 cm. Person B used a ruler with markings every 0.1 cm.
   
   d. Person A rounded their measurement.

**Correct Answer:**
   
   d. Person A rounded their measurement.

### Explanation:

The difference in measurements arises from how the precision of the measurements is recorded:

- **Student A's Measurement (1.5 cm):** 
  - Rounded measurement.
  - Indicates that the measurement was rounded to the nearest tenth of a centimeter (0.1 cm).

- **Student B's Measurement (1.50 cm):** 
  - More precise.
  - Measurement is to the nearest hundredth of a centimeter (0.01 cm).

In science and engineering, the precision of a measurement often includes all known digits plus one estimated digit. Hence, it's essential to be aware of the precision and accuracy of the instruments being used and to record measurements accordingly.
Transcribed Image Text:### Measurement Accuracy and Precision In this example, we examine the measurements taken by two students to understand the concepts of accuracy and precision in measurement: **Problem Statement:** 1. **Scenario:** - Student A measures an object and records a value of 1.5 cm. - Student B measures the same object and records a value of 1.50 cm. Both students have performed their measurements correctly. Why do these measurements differ? **Multiple Choice Answers:** a. They aren't different. b. Person A used a ruler with markings every 0.1 cm. Person B used a ruler with markings every 0.01 cm. c. Person A used a ruler with markings every 1 cm. Person B used a ruler with markings every 0.1 cm. d. Person A rounded their measurement. **Correct Answer:** d. Person A rounded their measurement. ### Explanation: The difference in measurements arises from how the precision of the measurements is recorded: - **Student A's Measurement (1.5 cm):** - Rounded measurement. - Indicates that the measurement was rounded to the nearest tenth of a centimeter (0.1 cm). - **Student B's Measurement (1.50 cm):** - More precise. - Measurement is to the nearest hundredth of a centimeter (0.01 cm). In science and engineering, the precision of a measurement often includes all known digits plus one estimated digit. Hence, it's essential to be aware of the precision and accuracy of the instruments being used and to record measurements accordingly.
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