What Is the Standard Form of a Number?
The standard form of a number is representing larger numbers in a way that is easy to read and write. If a number is in the expanded form, then, the standard form will depict the number in a concise form.
The example shown in the image depicts the number 625 in the standard form as well as in the expanded form.
How Do We Write the Decimals in the Standard Form?
Decimals are the simplest form of fractions and hence, writing decimals in their standard form is:
Decimal numbers have 10 as the base and need a decimal dot (‘.’) for their representation, and the decimal separates the whole and the fractional parts of the decimal. For example, 316.558 is the standard form of the decimal number which can also be written as 3 hundreds, 1 tens, 6 ones, 5 tenths, 5 hundredths and 8 thousandths.
Solved Examples
Example 1: Can you identify if the following number is written in scientific notation? \(4.2 \times 10^{-6}.\)
Solution:
Here, we can observe that in the given numerical expression, the factor 4.2 is at least 1 and less than 10 and the power of the base 10 has a ‘non-zero’ integer exponent.
So, the number is represented in the scientific notation.
Example 2: Write \(3.5 \times 10^{4}\) in standard form.
Solution:
\(3.5 \times 10^{4} = 35000\) [Moving decimal point 4 places to the right]
Hence, the standard form of \(3.5 \times 10^{4} = 35000\)
Example 3: Write the number in standard form. \(24 \times 10^{-5}\)
Solution:
\(24 \times 10^{-5} = 0.00024\) [Moving decimal point |-5| = 5 places to the left]
Hence, the standard form of \(24 \times 10^{-5} = 0.00024.\)
In order to write the standard form of a number, multiply any number between 1.0 to 10.0 by a power of 10. For example 20, 345, and 0.12 are numbers in the standard form.
The first digit of a particular decimal number is written followed by a decimal point and the rest of the digits and multiplied by a power of 10, such that when simplified, it generates the original value.
A number can be written in expanded form by splitting the number on the basis of place value.
For example: 231 can be written in the expanded form as ‘200 + 20 + 1’.
A number can be written in the scientific notation as a product of a factor or coefficient, and a power of 10. Here, the factor should be equal to or greater than 1 and less than 10, and the power of base 10 must be a non-zero integer.