Physics · Class 11

Significant figures

Leading zeros locate the decimal point; they are not significant. Zeros between significant digits count, as do trailing zeros explicitly written after a decimal point. An integer such as 1200 is ambiguous without a precision statement; scientific notation removes that ambiguity.

Open the interactive experiment →

Keep the digits your measurement supports.

தொடக்கப் பூஜ்யங்கள் முக்கிய இலக்கங்கள் அல்ல. முக்கிய இலக்கங்களுக்கு இடையிலுள்ள பூஜ்யங்களும் தசமப் புள்ளிக்குப் பின் எழுதப்பட்ட இறுதிப் பூஜ்யங்களும் கணக்கில் சேரும். அறிவியல் குறியீடு துல்லியத்தைத் தெளிவுபடுத்துகிறது.

Key notes, relationships and model limits

Key relationship

Addition/subtraction: retain the least precise decimal place. Multiplication/division: retain the fewest significant figures.

Remember

0.00450 has three significant figures. Write ambiguous integers such as 1200 in scientific notation with the intended precision.

Common trap

0.00450 has three significant figures. The initial zeros do not count, but the final zero does.

Model limits

Exact counts and defined conversion factors do not limit significant figures. Round the final result, rather than each intermediate step.

What you will learn

Count significant figures, use scientific notation, round with stated tie convention, and apply operation-specific rules.

Try the experiment

Type a measurement and choose retained figures. Exact decimal rounding uses nearest, ties to even; the rule is shown.

Think of it this way

Writing more digits is like adding more marks to a blurry photograph: the marks cannot create information that was not measured.

Worked example

2.345 to three significant figures is 2.34 using ties-to-even; 2.355 becomes 2.36. For addition/subtraction retain the least precise decimal place; for multiplication/division retain the fewest significant figures. For example, 12.11 + 0.3 = 12.41 is reported as 12.4; 2.4 × 3.12 = 7.488 is reported as 7.5. Round final results, not every intermediate step.

Why this matters

Exact counts and defined conversion factors do not limit significant figures. A measured value does. A zero reading needs an explicit resolution statement.

Before you start

Decimals · fractions · powers of ten

Check your understanding

How many significant figures does 0.00450 have?

Two
Three
Five

Read the explanation

The significant digits are 4, 5 and the final 0. Leading zeros only locate the decimal point.

Course connection: CBSE XI Chapter 1; NEET/Main Unit 1; JEE Advanced General. Depth and exam wording differ.