How do you calculate Order of Magnitude? Step-wise Solution

How do you Calculate Order of Magnitude?

Introduction

As you have already learnt about the basic definition of order of magnitude. Now we will provide you information and rules about how to calculate order of magnitude easily.

How to find the Order of Magnitude?

The order of magnitude gives the rough idea about the size or length of any physical quantity. It can be calculated by using scientific notation. A number is written in scientific notation then the order of magnitude is calculated by identifying the power of 10. See the following steps to find the order of magnitude of any number easily.

Order of Magnitude Calculations Steps

To calculate the order of magnitude any number, follow the given steps that make it easy.

1. Write the number in scientific notation by moving the decimal to non-zero number. Move the decimal to the right side if there are leading zeros and to the left side if there are trailing zeros.
2. Put the decimal just after the first non-zero number.
3. See the range 0.5< n ≤ 5 while placing the decimal.
4. If the first non-zero digit is 5 or greater than 5, you can put the decimal before it. But if the first non-zero digit is less than 5, you cannot put the decimal before it.
5. Count the digits that you skipped while moving the decimal point.
6. Write the number in scientific notation with the power of 10. The power of 10 is the order of magnitude.

The above steps help to calculate order of magnitude more easily than finding it by guessing. Let’s see the following examples to find the order of magnitude.

Examples of Order of Magnitude

• Suppose a number 5234, it can be expressed as 0.5234 because it satisfies the range of order of magnitude. So by using scientific notation,
$$5234\;=\;0.5234\;×\;10^4$$
• The number 0.35 can be expressed as 3.5 so,
$$0.35\;=\;3.5\;×\;10^{-1}$$

Since we moved to the right side, the order of magnitude is negative.

• In other examples, suppose the number 0.95. Since it is already in the range of 0.5< n ≤ 5 so.
$$0.95\;=\;0.95\;×\;10^0$$

Hence the order of magnitude of 0.95 is zero.

• Suppose a smaller number as 0.00000047, let’s see how much order of magnitudes in this number. We can write it as: 0.47. So,
$$0.00000047\;=\;4.7\;×\;10^{-7}$$

So the order of magnitude is -7

Real life Examples of Order of Magnitude

In many real life examples, length, mass, velocity etc. of different big and small objects are measured in order of magnitude. So that we can easily approximate them. Some of these examples are

• Mass of Earth that is 5.97219 × 10²⁴kg, It has 24 orders of magnitude. Imagine how big that number is.
• Speed of light is 2.99792458 × 10⁸ms^-1, it has 8 orders of magnitude which means that multiplying 10 eight times to get the original number.
• Diameter of Sun is 8.6537 × 10⁵miles, it has 5 orders of magnitude.
• Similarly another popular example of order of magnitude is the distance between the Earth and the Moon that is 2.389 × 10⁵miles, It also has 5 orders of magnitude.

Let’s solve one of the real life examples to find order of magnitude.

What is the Order of Magnitude of the Seconds Present in a Day?

To find the order of magnitude of the seconds, we know that there are 14 hours in a day, 60 minutes in an hours and 60 seconds in a minute so,

$$1\;day\;=\;hours\;×\;minutes\;×\;seconds$$ $$1\;day\;=\;24\;×\;60\;×\;60\;=\;86400\;sec$$

So there are 86400sec in a day. Let’s find its order of magnitude. We can write the number in scientific notation as 0.86400

$$86400\;=\;0.864\;×\;10^5$$

So the order of magnitude of seconds is 5.

How to arrange Fractions in Ascending Order of Magnitude?

Fractions are converted into decimal form to arrange them in ascending order. For example if you have a set of fractions as 24 / 47,36 / 71,60 / 117,84 / 169, in order to arrange them in ascending order of magnitude,

$$\frac{24}{47}\;=\;0.5106$$ $$\frac{36}{71}\;=\;0.5070$$ $$\frac{60}{117}\;=\;0.5128$$ $$\frac{84}{169}\;=\;0.4970$$

In ascending order, the numbers are arranged from lowest to highest. So according to the decimal parts of the fractions,

$$0.4970\;<\;0.5070\;<\;0.5106\;<\;0.5128$$

So, ascending order of magnitude,

$$\frac{84}{169}\;,\;\frac{36}{71}\;,\;\frac{24}{47}\;,\;\frac{60}{117}$$

FAQ’s,

What is the order of magnitude of 49?

The order of magnitude of 49 is 2. It is because when we move the decimal point to left side, 2 digits are skipped. The number of digits that we moved is the order of magnitude of 49.

What is Correct Scientific Notation?

The scientific notation is a way of writing a very small or a very large number to approximate them easily. The number is written in the power of 10 in scientific notation. The proper format of scientific notation is

$$N\;=\;n\;×\;10^x$$

What is the Order of Magnitude of 500000?

The order of magnitude of 500000 is 0.5 × 10⁶.