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Standard form calculator converts any number to standard form or scientific notation. It accepts number notation, e-notation, and scientific notation.
|Standard Form||3.456 × 108|
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This calculator converts input numbers to standard form or standard notation. The calculator takes positive or negative decimals and integers as inputs.
To use this standard form converter, enter the given number into the input field and press “Calculate.”
In simple words, a number is in standard form if it consists of a decimal number greater than zero and less than ten and (though not always) 10 raised to some power. This notation is often used to describe very big or small numbers.
For example, the mass of the Earth is currently estimated to be 5,972,200,000,000,000,000,000,000 kg. Saying or even writing down this number is cumbersome, but in standard form, it can be written as 5.9722 × 10²⁴ kg! Note that this number consists of two parts – a decimal 0 < 5.9722 < 10 and 10 to the power of 24.
For an example of a very small number let’s look at the mass of a grain of sand. The average grain of sand is estimated to weigh about 0.0000128 kg. This number can be written as 1.28 × 10⁻⁵ kg in standard form. It consists of two parts – a decimal 0 < 1.28 < 10 and 10 to the power of -5.
The terms “standard form” and “scientific notation” describe the same thing. The term “standard form” is mainly used in the US and other countries following the US conventions. “Scientific notation” is largely used in the United Kingdom and other countries following the UK conventions. Therefore, while this standard notation calculator accepts “scientific notation” as an input, converting scientific notation to standard form will not change how the number is written.
Let’s look at the conversion algorithm in several examples. For an example of a very big number, let’s convert 34,000,000 to standard form. We will take the following steps:
For an example of a very small number, let’s convert 0.00065 to standard form. We will take the following steps:
Alternatively, the conversion process can be described as follows:
Let’s convert 456,000 to scientific notation following the alternative algorithm:
Since 0 multiplied by any number is still 0, it is also 0 when multiplied by 10 to any power. This means that 0 can be written in standard form in an infinite number of ways: 0 = 0 × 10⁰ = 0 × 10¹ = 0 × 10² = 0 × 10³ = …
Standard form, or scientific notation, is widely used by scientists, engineers, and even in everyday life to describe very small or very large numbers. Below are some examples of values that are often described in standard form: