Precision is how finely and repeatably a measurement can be made.
Precision How finely and repeatably a quantity can be measured.
Step 1: Something to Notice
Watch first. The explanation comes later.
A calculator turns 4.2 cm × 3 into 12.600000001. Writing that down claims a precision no ruler in the room can deliver.
How many of those digits are real?
Step 2: Find Out
Isolate the instrument and find how many digits each one can honestly justify.
Step 1 — Predict
A ruler marked in whole centimeters. How precisely can you report a length?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
Accuracy is closeness to the truth
A badly calibrated balance can be very precise and consistently a gram out.
Accuracy How close a measurement is to the true value.
Significant figures record the precision
A centimeter ruler supports about 4.2 cm — the marks plus one estimated digit.
Calculators invent digits
Dividing measured quantities gives ten digits, and they look just like the real ones.
So a result follows its weakest input
No more significant figures than the least precise measurement that went in.
Extra digits are a claim you cannot back
A ruler marked in millimeters cannot support an answer to a thousandth of a millimeter. The number of digits reported should match the precision of the instrument used.
Accuracy and precision are different
Accurate means close to the true value; precise means repeatable. A miscalibrated balance gives precise readings that are consistently wrong, which is the most dangerous combination.
Step 4: A Common Mistake
Lots of people think
“More decimal places means a better answer.”
Step 5: Why a Broken Clock Beats a Slow One, Sometimes
The same idea somewhere new.
A stopped clock is exactly right twice a day; a clock losing a minute an hour is never right but is always close. Which is better depends entirely on what you need — an accurate reading occasionally, or a consistently wrong one you can correct for. A known systematic error can be subtracted out, which is why instruments are calibrated rather than discarded. Random error cannot be subtracted; it can only be averaged down by repeating.
Step 6: Think It Through
Practice makes it stick.
Four Decimal Places
Problem 1 of 2
You report 4.2847 cm from a ruler marked in centimeters. What is wrong?
The Consistent Balance
Problem 2 of 2
A balance reads 42.1387 g every time and is a gram out. Describe it.
Digits You Can Back
1 of 5
What is precision?
2 of 5
How many significant figures should a result carry?
3 of 5
4.2 cm × 3.15 cm × 2.0 cm to the right precision?
4 of 5
Which kind of error can be subtracted out?
5 of 5
How does a centimeter ruler support a tenth of a centimeter?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Is a result with more decimal places a better result?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain the difference between precision and accuracy, and why reporting extra digits is misleading.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- Precision is fineness and repeatability; accuracy is closeness to the truth.
- Significant figures record how precisely something was measured.
- A result carries no more significant figures than its least precise input.
- Systematic error can be corrected for; random error can only be averaged down.