# Rounding and Significant Figures

## Rounding and Significant Figures Revision

**Rounding and Significant Figures**

Being able to **round** to a certain number of **significant figures** is a vital skill that you will use in your experimental work and in your exams.

**Significant Figures**

In a number, the first digit that is **not **a zero is the 1^{\text{st}} **significant figure**. For example, the 1^{\text{st}} **significant figure** in 0.71 is the 7. The following digits after this 1^{\text{st}} one will always be the 2^{\text{nd}} significant figure, 3^{\text{rd}} significant figure etc, even if they’re zeros. So if a question was to ask you to give a calculation to 2 **significant figures**, you would round the number so that there is only the 1^{\text{st}} and 2^{\text{nd}} **significant figures** (as well as any zeros **before** the 1st significant figure).

See below a list of numbers, and how they have been rounded to 2 and 3 significant figures.

Number |
To \boldsymbol{2} \: \textbf{s.f} |
To \boldsymbol{3} \: \textbf{s.f} |

0.7134 | 0.71 | 0.713 |

6832 | 6800 | 6830 |

117 | 120 | 117 |

4.55 | 4.6 | 4.55 |

0.00489 | 0.0049 | 0.00489 |

56.5 | 57 | 56.5 |

235 600 000 | 240 000 000 | 236 000 000 |

0.06347 | 0.063 | 0.0635 |

It is important to always clarify how many significant figures you have **rounded** to in an answer. The clearest way to do this is write your answer and follow it with “to 3 s.f”, for example.

**Decimal Places**

You should already know how to round to** decimal places**, but here is a reminder in case you have forgotten.

Rounding to **decimal places** is different than rounding to significant figures. Rounding to decimal places means writing a number with a certain amount of numbers after the decimal point.

For example, if we wanted to round 5.3423 to 2 decimal places, it would be 5.34.

See below some different numbers rounded to 2 and 3 decimal places.

Number |
To \boldsymbol{2} \: \textbf{d.p} |
To \boldsymbol{3} \: \textbf{d.p} |

0.7134 | 0.71 | 0.713 |

2.2362342 | 2.24 | 2.236 |

0.005 | 0.01 | 0.005 |

4.5537 | 4.55 | 4.554 |

0.0234 | 0.02 | 0.023 |

**Example 1: ****Significant Figures**

A car of mass 1200 \: \text{kg} moves with an acceleration of 3.8 \: \text{m/s}^2. Calculate the acceleration of the car and give your answer to** \boldsymbol{2} significant figures**.

Use the equation F = ma.

**[2 marks]**

F = 4600 \: \text{N} to 2 s.f.

**Example 2: ****Significant Figures**

Calculate the resistance of a bulb if the current through it is 8.0 \: \text{A} and it’s potential difference is 6.5 \: \text{V}. Give your answer to \boldsymbol{2} **significant figures**.

Use the equation R = \dfrac{V}{I}.

**[2 marks]**

R = 0.81 \: \Omega to 2 s.f.

**Example 3: ****Significant Figures**

A student wants to investigate the **rate of photosynthesis** from a piece of pondweed that is submerged in water. They counted 25 bubbles emerging from the pond weed in 1 minute. Calculate the rate of photosynthesis in bubbles per second. Give your answer to \boldsymbol{2} **significant figures**.

**[2 marks]**

\dfrac{\textcolor{00d865}{25}}{\textcolor{2730e9}{60}} = 0.4166666....

\text{Rate of Photosynthesis} = 0.42 \: \text{Bubbles per Second} to 2 s.f.

## Rounding and Significant Figures Example Questions

**Question 1:** A student calculates the current through a component to be 0.02563 \: \text{A}. State this current to 1 significant figure.

**[1 mark]**

**Question 2:** Round the following numbers to 2 significant figures:

**a)** 0.00342

**b)** 1 646 000

**c)** 0.1

**Question 3:** A student wants to find the density of an object and calculates it to be 8.533 \: \text{kg/m}^3.

The student rounds their calculation to 8.5 \: \text{kg/m}^3. Have they rounded the number to 2 significant figures or 2 decimal places?

**[1 mark]**

The student has rounded the number to 2 significant figures.

8.53 would be the number rounded to 2 decimal places.