Standard form of numbers is used to denote a larger or
smaller number in a shorten form. In fields like mathematics, physics, and
engineering where large and small numbers are frequently utilized, it is very
helpful.
Standard form uses the power of 10 to express numbers, which
makes arithmetic and comparisons easier. The purpose of standard form, how to
convert a number into standard form, and the significance of standard form in
practical applications are all covered in this article.
What is standard form?
Standard
form is a means to express numbers that are either too big or too little to
be conveniently represented in normal decimal form. It is also known as
scientific notation or exponential notation. A number is stated using standard
form by multiplying a decimal number between 1 and 10 by a power of 10.
The decimal point must be shifted to the left or right a
certain number of times to return to the original value, which is represented
by the power of 10.
For instance, the conventional form of the number 5,400,000
is 5.4 x 106. The decimal number in this case is 5.4, and the power
of 10 is 6, meaning that to get the original value, the decimal point needs to
be shifted 6 places to the right.
The decimal point must be moved 5 places to the left to
reach the original value in the case of the number 0.000027, which may be
represented in standard form as 2.7 x 10-5. This is because the
decimal point is 2.7 and the power of 10 is -5.
Changing a Numerical value to standard from
We must carry out a few straightforward actions in order to
transform a number into standard form:
Decimal number identification:
- The first step is to recognize the decimal
number contained within the original number.
- The decimal number must range from 1 to 10. Count how many places the decimal point needs
to be shifted left or right in order to get the original value to determine the
power of 10.
- The power of 10 is negative if the decimal point
is moved to the left.
- The power of 10 is positive if the decimal point
is moved to the right.
Format the number as follows:
Put the decimal number in writing, then the power of 10 and
the letter "x" after it. For instance, the conventional form of the
number 12,345 is 1.2345 x 104.
Importance of a standard form
- Several real-world applications, particularly in
science and engineering where large and small numbers are frequently employed,
make use of standard form.
- Calculations, comparisons, and measurements
involving extremely big or extremely small numbers are made easier by using
standard form.
- Also, it enables scientists and engineers to
present their findings in a more condensed and uniform manner, facilitating the
understanding and replication of their discoveries by others.
Examples of Standard Form
Example 1:
Convert 345,000,000 to standard form
Solution
Step 1: Put
the decimal point after first significant digit.
3.45000000
Step 2: Count
the digits after decimal point and write them in the power of 10.
3.45000000 x 108
The decimal number is 3.45000000, and the power of 10 is 8,
so to get the original value, the decimal point must be shifted 8 places to the
right.
Step 3: Skip
the zeros.
3.45 x 108
You can also use online calculators to evaluate the standard
form of numbers.
Example 2:
Convert 0.00000034 to standard form
Solution
Step 1: Put
the decimal point after first significant digit.
00000003.4
Step 2: Count the number of decimal places to the right
of the last non-zero digit. In this case, there are 7 decimal places to the left
of the last non-zero digit.
00000003.4 x 10-7
Step 3: Skip
the zeros.
3.4 x 10-7
Example 3
Convert this into standard form 12345.67
Solution
Step 1: Put
the decimal point after first significant digit.
1.234567
Step 2: Count the number of decimal places to the right
of the last non-zero digit. In this case, there are 8 decimal places to the
right of the last non-zero digit.
12345.67 x 104
Example 4
Convert this into standard form 0.000000005.
Solution
Step 1: Put
the decimal point after first significant digit.
000000000.5
Step 2: Count the number of decimal places to the right
of the last non-zero digit. In this case, there are 8 decimal places to the left
of the last non-zero digit.
000000000.5 x 10-8
Step 3: Skip
the zeros.
5 x 10-8
Summary
In conclusion, the standard form is a helpful technique for
standardizing and compactly expressing very big or very small numbers. It is a
crucial tool in science, engineering, and mathematics since it makes
computations, comparisons, and measurements simpler.
Everyone working in these fields should be able to translate
numbers into standard form since it can improve the effectiveness of
communicating complex thoughts and findings.
