Precision vs Accuracy in Physics: Easy Guide with Examples | 9th Class PTCB 2025

Precision vs Accuracy in Physics: Easy Guide with Examples | 9th Class PTCB 2025

1.12 Precision and Accuracy 🎯 Introduction: Two Important Concepts 🤔

A physical measurement should be precise as well as accurate. These are two separate concepts and need clear distinction.

Let's understand them with simple examples! 📏✨

What is Precision? 🔄

Precision refers to how close together a group of measurements are to each other.

Example: Your Daily Alarm ⏰

• Monday: Wake up at 7:00 AM
• Tuesday: Wake up at 7:00 AM
• Wednesday: Wake up at 7:00 AM

Result: HIGH PRECISION (consistent every time!) ✅

What is Accuracy? ✅

Accuracy refers to how close the measured value is to the true or accepted value.

Example: Thermometer Reading 🌡️

• Your thermometer shows: 38.5°C
• Hospital thermometer shows: 38.5°C

Result: HIGH ACCURACY (matches true value!) ✅

The Bullseye Illustration 🎯

The best way to understand these concepts is with arrows hitting a target!

Case A: High Precision, Low Accuracy 🏹

Figure 1.15-a: All arrows hit close to each other but far from bullseye

• ✅ Precise (arrows grouped together)
• ❌ Not accurate (far from center)

Example: A broken scale that always adds 2 kg

• Shows 67 kg every time (precise)
• But true weight is 65 kg (not accurate)

Case B: High Accuracy (on average) 🎯

Figure 1.15-b: Arrows are spread out but average position near bullseye

• ❌ Not precise (scattered)
• ✅ Accurate (average near center)

Example: Manual measurements

• 10.2 cm, 9.8 cm, 10.1 cm, 9.9 cm
• Average = 10.0 cm (true value!)

Case C: High Precision AND High Accuracy 🎯✨

Figure 1.15-c: All arrows hit close to each other AND near bullseye

• ✅ Precise (grouped together)
• ✅ Accurate (near center)

This is the GOAL! 🏆

How to Determine Precision 🔍 Key Factor: Least Count

Precision is determined by the instrument being used.

The smaller the least count, the more precise the instrument! 📏

Example: Measuring Length

• Ruler (least count = 1 cm): Measures 15 cm
• Vernier Caliper (least count = 0.01 cm): Measures 15.34 cm ✅ More precise!

How to Determine Accuracy ✅ Key Factors:

1. Fractional Uncertainty: Smaller = More accurate
2. Size of Object: Smaller objects need more precise instruments
3. Significant Figures: More sig figs = More accurate

Example:

• 5 cm (1 sig fig) - Less accurate
• 5.00 cm (3 sig figs) - More accurate ✅

Timing Devices ⏱️

Different devices for different time measurements!

1. Atomic Clock ⚛️

• Measures: Very short intervals
• Accuracy: 10⁻¹⁶ seconds
• Used in: GPS, scientific research

2. Digital Stopwatch ⏱️

• Measures: Short intervals (seconds/minutes)
• Accuracy: ± 0.01 s
• Used in: Sports timing, lab experiments

3. Analogue Stopwatch ⏲️

• Measures: Short intervals
• Accuracy: ± 0.1 s
• Used in: Basic timing, school labs

4. Ticker-Tape Timer 📏

• Measures: 0.02 s intervals
• Used in: Motion analysis, physics labs

5. Watch/Clock 🕐

• Measures: Hours, minutes, seconds
• Accuracy: ± 1 s per day
• Used in: Daily timekeeping

6. Pendulum Clock 🕰️

• Measures: Hours, minutes, seconds
• Accuracy: ± 1-2 s per day
• Used in: Traditional clocks (Big Ben)

7. Radioactive Decay Clock ☢️

• Measures: Thousands to millions of years
• Accuracy: ± 50 years
• Used in: Dating fossils, ancient artifacts

Example: Carbon-14 dating for Egyptian mummies (3,000 years old) 🏺

Quick Comparison Table 📊

Device Time Range Accuracy Use Atomic Clock ⚛️ Nanoseconds 10⁻¹⁶ s GPS, Research Digital Stopwatch ⏱️ Seconds ± 0.01 s Sports, Labs Analogue Stopwatch ⏲️ Seconds ± 0.1 s Basic timing Watch/Clock 🕐 Hours/Days ± 1 s/day Daily life Radioactive Clock ☢️ Years ± 50 years Archaeology

Key Takeaways 💡

✅ Precision = Consistency (measurements close to each other)

✅ Accuracy = Correctness (close to true value)

✅ Best case: High precision AND high accuracy 🎯

✅ Smaller least count = More precision

✅ More significant figures = More accuracy

✅ Choose the right timing device for your measurement!

Practice Questions 📝

Q1: A student measures 5 times: 10.2, 10.3, 10.2, 10.3, 10.2 cm. True value is 12.0 cm. Is this precise or accurate?

Answer: High precision (consistent), Low accuracy (far from true value)

Q2: Which is more precise: Ruler (1 cm) or Vernier Caliper (0.01 cm)?

Answer: Vernier Caliper (smaller least count!)

Remember! 🧠

"In measurements, be like an archer who consistently hits the bullseye - both precise AND accurate!" 🎯