What is meant by Significant Figures and Order of Magnitude?

What is meant by Significant Figures and Order of Magnitude?

Introduction

In many measurements of physical quantities, the terms significant figures and order of magnitude are mostly used. Learn what is meant by significant figures and the order of magnitude.

What are Significant Figures?

Any non-zero number is a significant figure. The idea behind significant figures is to ensure that your measurement is precise when you do a big computation and have a bunch of digits. For example, 73 has two significant figures. In another example, 404 has three significant figures. The rule behind this concept is that all zeros between significant numbers are also significant figures. The online sig-fig calculator also follow the same rule.

What is the Order of Magnitude?

The order of magnitude is an approximation of a physical quantity and is defined by the power of 10 which is near to the magnitude of that physical quantity. So for a number N, there will be a number x such that 0.5< n ≤ 5 expressed as

The value of x describes how many orders of magnitudes of a number are. It is used to make estimates and approximate comparisons in scientific notation. You can also calculate the order of magnitude online.

Difference between Significant Figures and Order of Magnitude

Although the concepts of significant figures and order of magnitude are used in scientific notation to better represent large and complex numbers, there are some differences between them. See the following difference table to understand their dissimilarities.

Examples of Order of Magnitude

These examples will help you to understand how to calculate the order of magnitude.

1. The number 8 can be written as
$$8\;=\;0.8\;×\;10^1$$

So 8 has 1 order of magnitude.

2. The number 43 can be written as
$$43\;=\;4.3\;×\;10^1$$

So 43 has 1 order of magnitude.

3. To express the number 57 in the form of order of magnitude, we can write it as 0.57 or 5.7. See the range 0.5< n ≤ 5 that confirms that we can use 0.57. So,
$$57\;=\;0.57\;×\;10^2$$

So 57 has 2 orders of magnitude.

4. Suppose another number as 0.000067. We can rewrite it by using the range 0.5 < n ≤ 5,
$$0.000067\;=\;0.67\;×\;10^{-5}$$

The negative sign indicates that the number is very small.

Examples of Significant Figures

1. If we have a number 847, so by the definition of significant numbers, we can tell that 847 has three significant figures.
2. Suppose another number 5006. The significant figures are 4 because zeros between non-zero numbers are also considered as significant figures.
3. In a number 500, there is only one significant number.
4. In 0.075, the significant numbers are two. It is because the zeros left to a number are not significant.

FAQ’s

How many significant figures does 0.0040 have?

Significant figures are non-zero digits in any number, but zeros after decimal point or with a non-zero digit are also significant. In 0.0040, there are two significant figures 4 and 0.

What do you mean by Significant Figures?

The significant figures are the certain digits in a number. For example, in 0.0058, the significant figures are two, because zeros do not explain anything about a number. They just tell either the number is smaller or bigger.

What are the 5 Rules for Significant Figures?

The rules are

• All non-zero numbers are significant.
• Zeros between two non-zero numbers are significant.
• Leading zeros are not significant.
• Trailing zeros are significant.
• Trailing zeros in a whole number with the decimal are significant.

How many Significant Figures are there in 10?

There are two significant figures in 10, because the zero is on the right side which is trailing zero.