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1.1.3

Significant Figures & Rounding

Chapter 1 · Number Operations

1.1.3  Significant Figures & Rounding

Every digit in a measurement carries meaning — except the zeros that are just holding a place. Significant figures are how you tell the two apart, and rounding is how you keep only the ones you trust.

🎯 By the end of this you can…

  • ✓Count the significant figures in any number, including tricky trailing zeros
  • ✓Round a number to a given number of significant figures
  • ✓List every possible number of significant figures a whole number could have been given to

💡 The idea

Significant = trusted

The significant figures of a number are the digits that actually carry information about how precisely it was measured. has four significant figures — every digit counts.

📋 The five rules

  1. 1
    Every non-zero digit is always significant. ( s.f.)
  2. 2
    A zero between two non-zero digits is significant. ( s.f., but s.f. — the leading zeros don't count)
  3. 3
    In a decimal, zeros after a non-zero digit are significant. ( s.f.)
  4. 4
    In a decimal, zeros before the first non-zero digit are never significant — they're just placeholders. ( s.f.)
  5. 5
    In a whole number, trailing zeros are ambiguous — they might or might not be significant. It depends entirely on how precisely the number was actually measured.

✏️ Worked example

How many significant figures does 0.028 030 have?

  1. 1
    The leading is never significant (rule 4) — skip past it.
  2. 2
    Starting from the first non-zero digit, every digit counts, including the zeros sitting between or after non-zero digits: .

✅ Answer: 5 significant figures

🧮 143 200 is correct to x significant figures — list every possible x

1
If only the digits before the trailing zeros are trusted: is significant, the last two zeros are just placeholders → 4 s.f.
1 / 4

💡 The idea

Rounding keeps only the trusted digits

To round to significant figures: count digits starting from the first significant one, then look at the next digit. 5 or more → round the last kept digit up. Less than 5 → leave it. Every digit after that becomes a placeholder zero (or is simply dropped, after the decimal point).

✏️ Worked example

Round 503.88 to 4 significant figures

  1. 1
    The first 4 significant digits are .
  2. 2
    The next digit is , which is 5 or more, so round the 4th kept digit up: .

✅ Answer: 503.9

⚠️ The classic trap

Rounding to 3 s.f. looks like it should just trim digits, but the rounding carries all the way through: (3 s.f.) — the digit count still has to come out to exactly 3 significant figures, which is why the trailing is kept and written, not dropped.

🎮 Count them, or round them

⭐ 0 XP🔥 streak 0
1
How many significant figures in 39 018?
2
How many significant figures in 2900, correct to the nearest 10?
3
Round 728 to 2 s.f.
4
Round 0.003 018 5 to 4 s.f.
5
Round 6396 to 2 s.f.
6
How many significant figures in 7.020?
7
Round 0.004 512 to 2 s.f.
0 of 7 finished

🤔 143 200 has six digits total. Which number of significant figures is NOT possible for it?

🏅

You finished this lesson!

You can now read precision off a number the way it was intended — and that skill is exactly what the next lesson leans on when a word problem hands you an answer and asks "to how many significant figures?"

Keep reading — this lesson marks itself done automatically.