# Estimations

## Estimations Revision

**Estimations**

**Estimations** can be used to compare quantities, to check if our answers seem realistic and to help plan out experiments.

**Orders of Magnitude**

We can use **orders of magnitude** to estimate the size of an object or to compare two sizes. For example, we can estimate that the **mass** of the sun is about 10^{30} \text{ kg}. This represents roughly its mass to the nearest **order of magnitude**. However, its actual mass is slightly larger than this – approximately 1.989 \times 10^{30} \text{ kg}.

We can also compare numbers using **orders of magnitude**.

**Experimental Design**

Some of your AQA course relies on you understanding and applying **experimental techniques**. There are some specific key terms associated with **experimental design** that you should be familiar with:

**Dependent Variable**– this is the variable in the experiment that is measured.**Independent Variable**– this is the variable we are changing in our experiment.**Control Variables**– these are all the other variables we need to keep the same to ensure our experiment measures what we aim for it to measure.

When we create a results table, we usually follow the guidelines below. The **independent variable** is put in the first column and the repeats of the **dependent variable** are placed in the other columns.

Independent Variable |
Dependent Variable (Repeat 1) |
Dependent Variable (Repeat 2) |

Also, when drawing graphs we need to consider where we will place our variables. Usually we draw graphs in the form shown below:

**Example: Orders of Magnitude**

How many orders of magnitude bigger is the sun compared to Earth?

The mass of Earth is about 10 \textcolor{14cf11}{^{24}} \text{ kg}.

The mass of the Sun is about 10 \textcolor{125bc9}{^{30}} \text{ kg}.

**[1 mark]**

Therefore we can say that the sun is about \bold{10^6} times heavier than Earth.

This is an estimate as we have not used exact values but estimates can be useful and save time and calculations.

## Estimations Example Questions

**Question 1:** The diameter of the Sun is 1.4 \times 10^6 \text{ km} and the diameter of the Earth is 1.2 \times 10^4 \text{ km}. Compare these two values in terms of orders of magnitude.

**[1 mark]**

In terms of orders of magnitude, the diameter of the Sun is 10^6 \text{ km} and the diameter of Earth is 10^4 \text{ km}.

So the Sun is approximately \bold{10^2 \text{ km}} larger in diameter than Earth.

**Question 2:** You are asked to conduct an experiment to determine the effect of the length of a wire on its resistance. What would your independent, dependent and control variables be?

**[3 marks]**

Independent Variable: **length of wire** \textbf{(m)}.

Dependent Variables: **current** \textbf{(A)} and **voltage** \textbf{(V)}.

Control Variables: **temperature of wire, thickness of wire, material of wire, equipment**.

**Question 3:** Design an appropriate table to collect results from the above experiment.

**[3 marks]**

Length (m) | Current 1 (A) | Voltage 1 (V) | Current 2 (A) | Voltage 2 (V) | Current 3 (A) | Voltage 3 (V) | Average Current (A) | Average Voltage (V) |

**1 mark** for independent variable in left column.

**1 mark** for repeat readings of dependent variables.

**1 mark** for averages columns.

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