3 Ways to Write Numbers in Standard Form

Standard Form

Before getting towards the types of expressing standard form, it is important to know what is the standard form. If you have a very huge or complex number such as 12345678900000 or 0.000000002345678, then it will be very difficult to read them. But no worries! We can make it easy to read by expressing them in standard forms.

It is a format in which you have to put a decimal between 1.0 and 10.0 and then multiply it by a power of 10, for example:

1.98 ✕ 10¹³
0.76 ✕ 10¹³

However, any precise standard notation calculator is the best way to convert numbers into standard form without any error.

In what manner to define numbers in the standard form?

Follow some simple steps explained below to express a number into standard form

Let us suppose number: 81 900 000 000 000
Just write the first number that is 8
According to the above-described rule, just place a decimal after 8, It will be at 8.
Now count the digits that are present after 8. In this case, there are 13 digits.
Now, by using the power of 10, it expresses the number as 8.19 × 10¹³. This is the standard form. Note a rounding number calculator can also handle such a long number before converting them into standard form.

Now if you have a number that starts with zero such as 0.000 001 2, then you can express it as follows:

Point the first non-zero digit. In this case, it is 1.
Place the decimal after it (1.).
Count the digits before the decimals. In this case, they are 6 zeros. You have moved to the right so that it will be expressed in the negative form.
Its Standard form will be: 1.2 ×10ˉ⁶
In the case of 10ˉ⁶ -6 is the exponent of 10. Whenever you have to deal with exponents, an exponential number calculator is an efficient tool to handle such complex calculations.

Three common ways to write numbers in standard form

Below are some common ways to express your numbers in standard form. Have a look!

Standard form in case of Equation

If you have given any expression such as:

any sort of expression = 0
In such situations, digit 0 is present on the right side, whereas every other number is on the left side of the equation. For example, if we have to put x2 = 7 into Standard Form then we can express it as follows:
x2 − 7 = 0

Standard form in case of Polynomial

It is a very sophisticated way to express the Standard Form in which you will write down the term or digit that has the highest value. For example, consider an equation such as x2 when there is no other variable. Now based on this method, you will write 2 before X as it has the highest degree then X.

Take another example:

3×2 − 7 + 4×3 + x6
The highest degree in this scenario is 6. Therefore it will be written first. 3 and 2 and will come after it. Constant will be written in the last:
x6 + 4×3 + 3×2 − 7

Standard Form of a Decimal Number

Another common way to express the standard form is as follows:

If you have a certain number, let us suppose it’s 5326.6, then it will be written as 5.3266 × 103.
The reason for this phenomenon can be explained as:
5326.6 = 5.3266 × 1000 = 5.3266 × 103.

For converting from scientific notation to standard form, there are many tools available online. They operate free of cost. All you have to do is to write in a scientific notation calculator and hit the calculate button. They will give you the most accurate results for the given inputs in the blink of an eye.