What is an order of magnitude?

A power of ten used to express the approximate size of a physical quantity.

When a value lies between two powers of ten, how do you determine which order of magnitude is nearest?

By assessing whether the value is closer to the lower or upper power of ten on a logarithmic scale.

Why is the boundary between adjacent orders of magnitude located at approximately 3.16 times the lower power of ten?

Because the geometric mean of 1 and 10 is √10 ≈ 3.16, which marks the midpoint on a logarithmic scale.

A value of 4 lies between 10⁰ and 10¹. Which order of magnitude is it closer to, and why?

It is closer to 10¹ (order of magnitude 1), because 4 exceeds the boundary value of approximately 3.16.

What is a derived estimate in the context of order-of-magnitude calculations?

An estimate obtained by combining estimated quantities using physical relationships to produce a new estimate to the nearest order of magnitude.

AQA A-Level Physics 7408

Measurements and Their Errors

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Measurements and Their Errors

Estimation of physical quantities

3 things to know
Papers 1 and 3

Overview

Working to an order of magnitude, and estimating a derived quantity from known values.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

How is the order of magnitude of a derived quantity estimated?

Numbers

Where does the boundary between adjacent orders of magnitude lie, and why?

Key term

What does it mean to estimate a quantity to the nearest order of magnitude?

Questions from this subtopic

Each one with the model answer underneath.

1
What is an order of magnitude?
Model answer
A power of ten used to express the approximate size of a physical quantity.
2
What does it mean to estimate a quantity to the nearest order of magnitude?
Model answer
To express the quantity as the closest power of ten.
3
When a value lies between two powers of ten, how do you determine which order of magnitude is nearest?
Model answer
By assessing whether the value is closer to the lower or upper power of ten on a logarithmic scale.
4
Why is the boundary between adjacent orders of magnitude located at approximately 3.16 times the lower power of ten?
Model answer
Because the geometric mean of 1 and 10 is √10 ≈ 3.16, which marks the midpoint on a logarithmic scale.
5
A value of 4 lies between 10⁰ and 10¹. Which order of magnitude is it closer to, and why?
Model answer
It is closer to 10¹ (order of magnitude 1), because 4 exceeds the boundary value of approximately 3.16.
6
What is a derived estimate in the context of order-of-magnitude calculations?
Model answer
An estimate obtained by combining estimated quantities using physical relationships to produce a new estimate to the nearest order of magnitude.

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