Decimals: Standard Form of Numbers & Scientific Notations

---

Writing the Standard Form of a Number

[Click Here for Sample Questions]

We can follow the given steps while writing the standard form of a Number:

Step 1: Write the number and add a decimal after the first digit of the number.

Step 2: Now, just count the number of digits after which the decimal has to be inserted and write the number in the power of 10.

Example: Let's take 5610000000 as an example number, Then the standard form of a number is:

Step 1: The first number is 5, add a decimal behind it. The number becomes 5.610000000

Step 2: Count the Number of digits after the decimal which is 9 in this case.

Hence, the number in the scientific form is " 5.61 × 10? "

Also Read:

---

Writing Standard Form of a Decimal Number

[Click Here for Sample Questions]

We can take different place values of the numbers to represent the number in its standard form. Decimal uses the base of 10, a set of 10 digits, and a dot for the representation of the standard form of a Decimal Number. For example, the number 564.122 can be written as 5 hundreds 6 tens 4 ones 1 tenth 2 hundredths and 2 thousandths.

Way to write the Decimal Number:

Step 1: Write the first non-zero digit from the number that you have chosen and then add a decimal point just after the first non-zero digit.

Step 2: The next step is to write the number in the power of 10.

Example: 0.0000037 in standard form is as follows:

Step 1: In the number, the first non-zero digit is "3", Add the decimal point after the digit "3".

Step 2: Here, the decimal point has shifted six places towards the right. Hence, the standard form of the chosen number 0.0000037 is 3.7 ×10^-6

Also Read: 

---

Expanded Form of Number

[Click Here for Sample Questions]

Now, let us consider a 7 digit number 5657891. Then the number in the expanded form will be:

5657891 = 6 × 100000 + 5 × 10000 + 7 × 1000 + 8 × 100 + 9 × 10 + 1

We can express this number in the exponential form as well, as we know that 10000=10⁴, 10 = 100, and so on.

5657891 = 5 × 10⁶+ 6 × 10⁵ + 5 × 10⁴ + 7 × 10³ + 8 × 10² + 9 × 10¹ + 1 × 10⁰

Read More:

---

Expanded Form of Decimal Number

[Click Here for Sample Questions]

We can also write decimal numbers in expanded form. And to do so, decimal into the expanded form, we have to multiply digits with the increasing exponents of 1/10 or 10-1.

Let us understand with the help of an example:

Example: Write 0.978 in expanded form.

0.978 = 9 × 10^-1 + 7 × 10^-2 + 8 × 10^-3

= 9 × 1/10 + 7 × 1/100 + 8 × 1/1000

= 0.9 + 0.07 + 0.008

Read more:

---

Writing Standard Form of a Rational Number

[Click Here for Sample Questions]

The rational numbers are written in the form of ‘p/q’ which is said to be in the standard form if the denominator q is positive and both the integers a and b have no common divisor other than 1. 

Steps to follow to convert a rational number to its standard form: 

• Write the chosen rational number. Check if the denominator is a positive or negative integer.
• If the number is negative, then we have to multiply both numerator and denominator by -1, to make the denominator positive.
• Now, find out the greatest common divisor (GCD) of numerator and denominator, which could be cancelled. The next step is to divide the numerator and denominator by GCD.

The number you got is the required standard rational number.

Read More:

---

Expressing Large Numbers in its Standard form

[Click Here for Sample Questions]

We can express any number as decimal numbers between 1 and 10 multiplied in powers of 10. Let's call for an example to understand. We can understand this concept with the following examples.

300 = 3 × 10²

367 = 3.67 × 10²

36.78 = 3.678 × 10¹

This kind of advancement in the field of science and technology has introduced us to numbers as big as the diameter of the Earth and also as small as the size of a human cell. So, to represent these numbers we use an exponential form of the number.

Read More:

---

Things to Remember

[Click Here for Sample Questions]

• Representation of any larger number in a smaller form using exponents and following some set of rules.
• Decimal uses the base of 10, a set of 10 digits, and a dot for the representation of the standard form of a Decimal Number.
• The rational numbers are written in the form of ‘p/q’ which is said to be in the standard form if the denominator q is positive and both the integers a and b have no common divisor other than 1.
• We can also say that writing a number in its standard form is the same as writing the number in its rational form i.e, p/q form.
• The standard form of the number is also considered the "scientific notation" of a given number as it plays a major role in making the large scientific number look smaller and easier to handle.

Read More: