Standard form is basically a method to write down big or very small values in an easy way, for example, you can write 1.9 × 106 in place of 1900000 and it is very useful in calculation and saves time for small values, it can also be written in the standard form its index will be in negative to show that it’s a small number.
A Persian mathematician named Muhammad Al-Khwarizmi in the early 9th century first introduced the term Standard form also called scientific notation it depends on the country and what they use the name scientific notation or standard form.
Moreover, in this article, with the help of basic definition rules and their use in daily life will be discussed also with the help of examples topic will be explained for better understanding.
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What is the Standard form of numbers?
The term standard form or scientific notation is a way to write huge or very less values in the easiest manner just by comparing the power of 10.
In mathematical form, it is written as
q × 10n
Here q is a number 1 ≤ q ≤ 9 and n is an integer.
Standard form plays an important role in a lengthy calculation like writing the mass of the earth there are 99% chances of mistakes if anyone writes it manually so similar to this there are many values that we can’t write without using a standard form. For example, the mass of the earth is “5972190000000000000000000” instead of this you can write “(5.97219 x 1024)”
Steps to convert in standard form
Suppose you have a number 6,78,000 to change it in standard form follow the steps below:
Step 1:
In the first step, we write the first digit
Step 2:
In the second step, write a decimal point after this with remaining non-zero numbers like 6.78
Step 3:
Finally, check how many numbers of digits you have passed to reach to place it here and then multiply that number with “raise to power ten
Step 4:
Remember moving from left to right then the index should be written with a negative sign and if moving from right to left then the index should be written with the positive sign
Step 5:
Hence the standard form for 678,000 is 6.78 × 10 5
To avoid these steps, try a standard form calculator which will give the desired result in a fraction of a second.
Examples of the standard form:
In this section with the help of examples, the topic is explained for better understanding.
Example 1:
Convert it 0.0000000321 into standard form
Solution:
Step 1:
From the question it is clearly shown that point is on the left side and to shift it after the first non-zero digit and here moving from left to right, then the index should be written in a negative sign
= 0.0000000321
Step 2:
The place of the decimal point should be checked first.
= 0.0000000321
Step 3:
Now move the decimal point after the first non-zero digit.
= 3.21
Step 4:
Finally, check how many numbers of digits you have passed to reach to place it after 1st non-zero digit and then multiply that number with “raise to power ten” in this problem to place it after the non-zero digit decimal point move 8 digits to the right side.
= 3.21 × 10-8 Answer.
Note:
If moved from left to right then the index should be written with a negative sign and if moved from right to left then the index should be in positive sign.
Example 2:
Convert 6,53,000,000,000 into standard form.
Solution:
Step 1:
From the question it is clearly shown that point is on the left side and to shift it before the last non-zero digit and here moving from right to left then the index should be written with a positive sign
= 653000000000
Step 2:
Check the place value of the decimal point,
= 653000000000
Note: there is no decimal point then it should place on most right side of the number.
Step 3:
Move the point to the right side of the 1st non-zero digit that is
= 6.53
Step 4:
Finally, check how many numbers of digits you have passed to shift it before the last non-zero digit here moving from right to left then the index should be written with a positive sign then multiply that number with “raise to power ten” in this problem to place it before last non-zero-digit decimal point move 11 digits to the left side.
= 6.53 × 1011 Answer.
Example 3:
Convert 3234561.64 × 105 in standard form.
Solution:
Step 1:
From the question it is clearly shown that point is on the left side and to shift it before the last non-zero digit and here moving from right to left then the index should remain in a positive sign
= 3234561.64 × 105
Step 2:
Check the place value of the decimal point,
= 3234561.64 × 105
Step 3:
Move the decimal point to the right side of the 1st non-zero digit that is
= 3.23456164
Step 4:
Finally, check how many numbers digits you have passed to shift it before the last non-zero digit here moving from right to left then the index should remain in a positive sign then multiply that number with “raise to power ten”
= 3.23456164 × 105 × 106
Here you see bases are the same then powers will be added.
= 3.23456164 × 105+6
= 3.23456164 × 1011
Which is the standard form of 3.23456164 × 1011
Summary:
- In this article, you have studied the basic use of standard form its need, and its importance in calculations furthermore with the help of an example topic is explained and after a complete understanding of this article, anyone can easily defend this topic and make his/her daily life calculation easier.
