Rounding Off Numbers To Significant Figures

Rounding off numbers to significant figures and decimal places are commonly asked questions in Maths exams.

In this tutorial, you will learn the rules of rounding off, the rules of significant figures and the steps to rounding off numbers to significant figures.

BONUS: A link to real past questions on significant figures is included at the end of this tutorial.

Meaning of Rounding off

Rounding off means making a number simpler but keeping its value close to what it was.

General Rules for Rounding Off

  • Start rounding off from the last digit of the number.
  • 5, 6, 7, 8, or 9 are rounded up to 1 and added to the next number on the left.

EXAMPLE:

38 rounded off to the nearest ten is 40.

  • 0, 1, 2, 3, or 4 are rounded down to 0

EXAMPLE:

33 rounded off to the nearest ten is 30.

Meaning of Significant Figures

Significant figures are usually the non-zero digits in a number. But sometimes, zeros can be significant depending on their position in the number.

Rules for Significant Figures

1. All non-zero digits ARE significant.

EXAMPLE:

The number 33.2 has THREE significant figures because all the digits are non-zero.

2. Zeros between two non-zero digits ARE significant.

EXAMPLE:

2051 has FOUR significant figures. The zero is significant because it is between non-zero digits of 2 and 5.

3. Leading zeros are NOT significant. 

EXAMPLE:

0.54 has only TWO significant figures and 0.0032 also has TWO significant figures because all of their zeros are leading.

4. Last zeros are ONLY significant if the number contains a decimal

EXAMPLE:

540. has THREE significant figures but 540 has TWO significant figures.

And 0.0300 has THREE significant figures.

Rounding Off numbers to Significant Figures

Questions on rounding off numbers to significant figures are always asking you to reduce the number of significant figures in that question.

  • QUESTION 1: Correct 0.3254 to 2 significant figures.

1. Take note of the number of significant figures.

EXAMPLE:

0.7251 has FOUR significant figures.

However, the question asked us to make it TWO significant figures

2. Start from the last digit.

EXAMPLE:

0.7251

3. Round off from 4 To 3 significant figures

EXAMPLE:

0.7251 — FOUR significant figures (4 s.f)

= 0.725 — THREE significant figures (3 s.f)

4. Round off from 3 To 2 significant figures

EXAMPLE:

0.725 — THREE significant figures (3.s.f).

= 0.73 — TWO significant figures (2.s.f)

  • QUESTION 2: Express 47058 to 2 significant figures

Following the steps detailed above.

SOLUTION:

47058

= 47060 — FOUR significant figures (4 s.f)

= 47100 — THREE significant figures (3 s.f)

= 47000 — TWO significant figures (2 s.f)

  • QUESTION 3: Express 793.48 to 1 significant figure

SOLUTION:

793.48

= 793.5 — FOUR significant figures (4 s.f)

= 794 — THREE significant figures (3 s.f)

= 790 — TWO significant figures (2 s.f)

= 800 — ONE significant figure (1 s.f)

Summary on Rounding Off numbers To Significant Figures

  • 0, 1, 2, 3, or 4 are rounded down to Zero.
  • 5, 6, 7, 8, and 9 are rounded up to One.
  • All non-zero digits are significant.
  • Zeros between non-zero digits are significant.
  • Leading zeros are not significant
  • Last zeros are only significant if there is a decimal point.

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