Order of Magnitude Calculator

Calculating the estimated order or size of a physical quantity is not an issue because of our order of magnitude calculator.

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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.

Order of Magnitude Calculator with Steps

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 3.4×10¹⁶, as you see the given number is already in scientific notation.

So, the order of magnitude of 3.4×10¹⁶ is 10¹⁶. 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 10¹⁶.

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 10³ 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.

Related References

How would you define order of magnitude?
Explain the solve order of magnitude problem. Explain in detail.
Give some examples of order of magnitude:
Give an overview of order of magnitude?

Frequently Ask Questions

How do i calculate order of magnitude between two numbers?

To calculate the order of magnitude between two numbers, you can follow these steps:

Find the powers of 10 that are closest to each number. It determines the exponent in scientific notation for numbers.
It subtracts the exponent of the powers of 10 to compare two numbers.
The difference in exponents gives you the order of magnitude between the two numbers.

For example, let's have two numbers: 5000 and 0.005.

For 5000: 5000 is closest to 10⁴ in scientific notation, its exponent is 4.

For 0.005: 0.005 is closest to 10⁻³ in scientific notation, its exponent is −3.

Now, subtract the exponents:

$$ 4−(−3) \;=\; 4 + 3 \;=\; 7 $$

So, the order of magnitude between 5000 and 0.005 is 7.

How many orders of magnitude is 20 times?

To determine how many orders of magnitude 20 times is, you need to express 20 as a power of 10 in scientific notation. 20 can be shown as 2 × 10¹ scientific notation. Since 20 already has a power of 10, multiplying it by 10 will increase the exponent by 1. So, multiply 20 by 10 and the result is 200, which is 10 times 20 then the order of magnitude is 1.

How many orders of magnitude larger is 7250m that 83m?

To find out the orders of magnitude larger than 7250 meters than 83 meters, you need to compare the magnitudes using scientific notation. It expresses 7250 and 83 meters in scientific notation: 7250 meters is approximately 7.25 × 10³ meters and 83 meters is approximately 8.3 × 10¹ meters. To find the difference, subtract their exponents:

$$ 3 − 1 \;=\; 2 $$

Therefore,7250 meters is 2 orders of magnitude larger than 83 meters.

How many orders of magnitude larger 0.25?

To calculate the orders of magnitude larger than 0.25, write the integer 0.25 in scientific notation.

$$ 0.25 \;=\; 2.5 × 10^{−1} \;in\; scientific\; notation $$

Compare this to 1 in scientific notation (1 × 10). Its exponent power for 0.25 is −1. Therefore, 0.25 is 1 order of magnitude smaller than 1.

How much is a order of magnitude of 10?

An order of magnitude of 10 shows when you increase a quantity by one order of magnitude, then you multiply it by 10. For example, If you have 10 then increase it by one order of magnitude, you get 100. Same for 100, increase it by one order of magnitude, you get 1000.

If you have 1000 then increase one order of magnitude, you will get 10000, and so on. When you decrease a quantity by one order of magnitude that means dividing it by 10. Therefore, an order of magnitude of 10 shows a significant change in scale, either increasing or decreasing with a factor of 10.

Amanda Jepson

Last Updated February 21, 2024