## Introduction to the Order of Magnitude Calculator

Order of magnitude calculator is an online tool that helps you to **find the estimated order** or size of a physical quantity. Our tool determines the two quantities when you compare them with the fixed ratio of ten to get a rough idea about the weight or size of the amount given.

## What is an Order of Magnitude

Order of magnitude is defined as the **size of a number** which may be larger or smaller than a physical quantity. It is an exponential power of ten when you convert it into scientific notation and then round off the given number to get the order of magnitude.

## Formula of Order of Magnitudes

The** Formula of an order of magnitude** has an integer number N which may be negative or positive depending on the given number. The formula of the order of magnitudes used by the Order of magnitude calculator is given below,

$$ N.d \times 10^n $$

d is the number that comes after the decimal point, later it will round off as per the given integer behavior. 10 is the base on which the order of the magnitude find and n is its exponential power.

## How to Calculate Order of Magnitude

Order of magnitudes can be calculated with the help of a given formula used by the orders of magnitude calculator that converts integers into scientific notation with factor base 10.

You can easily understand the **order of magnitude method** with the help of an example that compares two numbers to find their order in a stepwise process.

### Example:

Find the estimated order of magnitudes of 123 multiplied by 456 in steps.

**Solution:**

The steps to estimate orders of magnitude are,

**Step 1**:

First, write down the given numbers in scientific notation:

$$ 123 \;=\; 1.23 \times 10^2 $$

$$ 456 \;=\; 4.56 \times 10^2 $$

**Step 2**:

Then multiply these numbers as per the given condition in question

$$ (1.23 \times 10^2) \times (4.56 \times 10^2) \;=\; (1.23 \times 4.56) \times 10^2 + 2 \;=\; 5.6208 \times 10^4 $$

**Step 3**:

To find the order of magnitudes, we round off the multiplication result 5.6208 to 6, because it's closer to 6 on the number line as

$$ 5.6 ≥ 5 $$

**Step 4**:

So, the order of magnitude of 123 multiplied by 456 is approximately 10^4, which gives the size of the given number without calculating the exact value.

## What is the Order of Magnitudes of 3.4 x 10^16

To find the order of magnitude of 3.4×10^{16}, as you see the given number is already in scientific notation.

So, the order of magnitude of 3.4×10^{16} is 10^{16}. The order of magnitude calculator tells that the given number has a very large value when 3.4×10^16 is on the order of 10^{16}.

## How is 500 3 Orders of Magnitude

To understand how **500 is three orders of magnitude**, the order of magnitude online calculator compares it to the given value that is 10^{3} times smaller.

Let's take 500 as our reference value.

$$ 500 \times 10^0 \;=\; 500\; (1st\; order\; of\; magnitude) $$

$$ 500 \times 10^1 \;=\; 5000\; (2nd\; order\; of\; magnitude) $$

$$ 500 \times 10^2 \;=\; 50000\; (3rd\; order\; of\; magnitude) $$

So, when the values are compared, then the result is an increase of 500 by three orders of magnitude which is 50000, which means that 500 is three orders of magnitude smaller than 5000.

## How many Orders of Magnitude is 45 to 19,000

For the calculation of **orders of magnitude between 45 and 19,000**, the order of magnitude solver writes them in scientific order and compares them,

**For 45**:

$$ 45 \;=\; 4.5 \times 10^1 $$

**For 19,000**:

$$ 19,000 \;=\; 1.9 \times 10^4 $$

Now, their exponent's power has a difference

$$ 4−1 \;=\; 3 $$

So, there are 3 orders of magnitude between 45 and 19,000.

## How to Use Order of Magnitude Calculator

The orders of magnitude calculator has a simple design tool that enables you to use it to calculate the order of two numbers when you compare them.

Before adding the **input function to the order of magnitude** online calculator, you must follow some simple steps so that you get a wonderful experience during the calculation. These steps are:

- Enter the number in which order you want to find in the input box.
- Review your number before hitting the calculate button to start the evaluation process of order of magnitude.
- Click the “Calculate” button to get the result of your given number problem
- If you want to try out our order of magnitude solver for the first time then you can use the load example to get a better understanding of the concept of the order of magnitude method.
- Click on the “Recalculate” button to get a refresh page for more example solutions of integer problems.

## Final Result of Orders of Magnitude Calculator

The order of magnitude calculator gives you the **solution to the order of magnitude** problem when you add the input of two numbers into it. It provides you with solutions with a complete procedure. It may be included as:

**Result Option**

When you click on the Result option it gives you a solution of integer to find the order

**Possible Steps**

It provides you with a solution in which all the evaluation processes are present in a step-by-step method when you click on this option.

## Benefits of Order of Magnitude Online Calculator

The orders of magnitude calculator provides you with **multiple benefits** whenever you use it to calculate the order of a given number of problems and give you a solution. These benefits are:

- It is a free-of-cost tool that enables you to use it free to find the number problem.
- It is a versatile tool that can manage various types of numbers to find the order of your number.
- Our order of magnitude solver helps to get a strong hold on the greater or smaller order of a given number concept when you use it to practice finding more examples.
- Our tool saves the time that you spend on doing the comparison between two number calculations to get more a number.
- It is a reliable tool that provides you with accurate solutions whenever you use it to calculate integers, fractions, or decimals without any error.
- The order of magnitude calculator provides the solution with a complete process in a stepwise method so that you get clarity on the order of magnitude problems.