Content Curator
Decimals and octal both come under the number system, so if one wants to convert decimals into octal, one has to first learn about the number system. The numbers are converted based on the number system.
- The conversion is done when we need to find the equivalent of any number.
- Each type of number system has its base number.
- For the conversion, the number is divided by the base number.
- The base number of decimals is 10, and the base number of octal is 8.
- As a result, to convert, one divides the number which is decimal by 8, as 8 is the base number of octal.
Read More: Decimal Expansion of Rational Numbers
| Table of Content |
Key Terms: Decimals, Octal, Number system, Base number, Hexadecimal.
Number System
[Click Here for Sample Questions]
A number system is a mode of representation of numbers either in the form of digits or symbols. There are various types of number systems like binary, decimals, octal, and hexadecimal, and decimals, and octal is two types of the number system that we will study today.
Decimal number
The number which has the base number 10 is known as a decimal.
- Decimals use ten digits which range from 0-9.
- They consist of integers lying on the number line.
- A decimal number has both integers and decimals, they are separated by a dot(.), the number on the left is an integer, and the number on the right is decimal.
- Example: (43.67)10, (9.3)10.
Octal number
The number which has the base number 8 is known as octal.
- Octal contains 8 digits which range from 0-7.
- For the octal number system to be represented in binary, just three bits are needed.
- Each place in this system is multiplied by 8 to determine its weight.
-
Example: (324)8, (54)8.
Read More: Bayes Theorem Formula
Steps to Convert Decimal to Octal
[Click Here for Previous Year Questions]
Here are the steps one needs to follow to convert the number from decimal to octal:
- First, write the decimal number which is given.
- If the decimal number given is less than 8, then the octal number will also be the same, and there is no need for conversion.
- And if the decimal number is greater than 7, then we need to divide the number by 8.
- The remainder is noted, and the quotient is further divided by 8, as many times till we get a quotient that is less than 8.
- The remainder which was noted down is now written in reverse order from the bottom to the top.
- The number we get is the octal number which is equivalent to the decimal number which was given.
For example:
| Decimal number | Operation (division) | Quotient | Remainder | Octal number |
|---|---|---|---|---|
| 1542 | 8 | 192 | 6 | 6 |
| 192 | 8 | 24 | 0 | 06 |
| 24 | 8 | 3 | 0 | 006 |
| 3 | 8 | 0 | 3 | 3006 |
Also Read:
| Related Articles | ||
|---|---|---|
| Decimals to Binary | Octal to binary | Hexadecimal to decimal |
Different Ways to Convert Decimal to Octal
[Click Here for Sample Questions]
There are various methods of converting decimals to octal which are given below:
- Successive multiplication by 8: This is an easy method of converting decimal fractions to octal.
- First, one needs to multiply the given decimal fraction number by 8.
- The number one gets after multiplying from it, the integer is the first digit of the octal number, and then multiply the fraction part of the number with 8, till it becomes null.
- Euclidean method of successive division by 8: in this method, the given decimal number is divided by the power of 8, and then divide the remainder with smaller powers of 8 till one gets 1.
- The octal number is the quotient which is written in the order which was attained while division.
- Indirect method: this is a method to convert decimals to octal by first converting the decimal number to another number system like binary or hexadecimal, then converting into binary from hexadecimal and using the grouping from the octal numbers.
Read More: Hexadecimal
Decimal to the Octal Table
[Click Here for Previous Year Questions]
Here, is the conversion table for decimal to octal number system–
| Decimal number | Equivalent octal number |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 3 |
| 4 | 4 |
| 5 | 5 |
| 6 | 6 |
| 7 | 8 |
| 8 | 10 |
| 9 | 11 |
Things to Remember
- To convert from decimal to octal, you need to keep in mind the number system.
- There are four types of number systems: binary, decimal, octal, and hexadecimal.
- The decimal number has a base number of 10, which ranges between 0-9 and the octal number has a base number of 8, which ranges between 0-7.
- For conversion, if the decimal number is less than 8, then there is no need to convert the octal number to is same as the decimal number.
- If the decimal number is greater than 7, then we need to divide the number by 8 to get the remainder and note it down and divide the quotient by 8 till the quotient is less than 8.
- Write the rest from the bottom to the top, and it is the octal number equivalent to the decimal number.
Previous Year Questions
- Which of the following is correct?...[JIPMR 2009]
- Fusion reaction takes place at high temperature because...[NEET UG 2011]
- Trien is...[AIIMS 2018]
- Sucrose on hydrolysis gives...[NEET UG 2020]
- Which of the following has zero dipole moment?...[NEET UG 1996]
- A disc of mass 2kg and diameter 2m is performing rotational motion. Find the work done, if the disc is rotating from 300rpm to 600rpm.
- The angle between two diagonals of a cube is….[KCET 2014]
- The electric field at a point is..
- Extraction of zinc from zinc blende is achieved by...[JEE Advanced 2007]
- The nucleic acid base having two possible binding sites is...[AIIMS 2004]
Sample Questions
Ques. What is a number system? (2 Marks)
Ans: number is a way of representing a number with the help of digits or symbols. There are four types of number systems: hexadecimal, octal, decimal, and binary.
Ques. What is a decimal number? (2 Marks)
Ans: decimal numbers are numbers that have both integers and decimals and have a base number of 10. For example, (23.4)10
Ques. What are octal numbers? (2 Marks)
Ans: octal numbers are number whose base number is 8, and it uses digits from 0 to 7. For example, (78)8
Ques. How to convert decimal numbers to octal numbers if the number is less than 8? (2 Marks)
Ans: if the decimal number is less than 8, then there is no need to convert, the octal number is the same as the decimal number.
Ques. Convert (156)8 decimal numbers to octal numbers. (5 Marks)
Ans: First, divide 156 by 8
= quotient (19) and the remainder (4)
= Again, divide 19 by 8
= Quotient (2), the remainder (3)
= Divide 2 by 8
= Quotient (0) and the Remainder (2)
Since the quotient is zero, we cannot divide anymore. So, writing the remainder in reverse order we get,
= (234)8
Hence,
(156)10 = (234)8
Ques. Convert the decimal number (200)10 to an octal number.
Ans: Divide 200 by 8
= 25 (quotient) and 0 (remainder)
= Divide 25 by 8
= 3 (quotient) and 1 (remainder).
= Divide 3 by 8
= 0 (quotient) and 3 (remainder).
Since the quotient is zero, we cannot divide anymore. So, writing the remainder in reverse order, we get,
= (310)8
Hence,
(100)10 = (310)8
Ques. Convert the decimal number (440)10 to an octal number. (3 Marks)
Ans: divide 440 by 8
= 55(quotient) and 0 (remainder)
= Divide 55 by 8
= 6 (quotient) and 7 (remainder)
= Divide 6 by 8
= 0 (quotient) and 6 (remainder)
Since the quotient is zero, we cannot divide anymore. So, writing the remainder in reverse order we get,
= (670)8
Hence,
(440)10= (670)8
Ques. How to convert decimal numbers to octal with a decimal point? (3 Marks)
Ans: to convert decimal to octal with a decimal point, we need to divide the number into whole numbers and fractions. First, divide the whole number by 8, till we get the quotient zero. Then, the answer will be the remainder written in reverse order from bottom to top. After that, take the fraction part and multiply by 8 till the result is zero. The octal number will be the first digit we get after multiplying. Then the final number is obtained by adding the fractional and whole numbers.
Ques. Convert decimal number (4321.356)10 into octal. (till 6 significant figures) (5 Marks)
Ans: First, let’s divide them into two parts whole numbers and fractions. Further, divide the whole number (4321) by 8
= 540 (quotient) and 1 (remainder)
= divide 540 by 8
= 67 (quotient) and 4 (remainder)
= divide 67 by 8
= 8( quotient) and 3 (remainder)
= Divide 8 by 8
= 1 (quotient) and 0 (remainder)
= Divide 1 by 8
= 0 (quotient) and 1 (remainder)
Since the quotient is zero, we cannot divide anymore. So, writing the remainder in reverse order we get,
= (10341)8
Now let’s convert the fraction part (0.356)
= multiply 0.356 *8
= 12.848
Octal no= 2
Then, multiplying 0.848 * 8
= 6.784
Octal no =6
Then, multiplying 0.784*8
= 6.272
Octal no= 6
Then, multiplying 0.272*8
= 2.176
Octal no= 2
Then, multiplying 0.176*8
= 1.408
0ctal no = 1
Then, multiplying 0.408*8
= 3.264
Octal no= 3
Hence the octal number up to 6 significant number is,
= (10341.266213)8
Ques. What is the indirect method of converting decimal numbers to octal numbers? (2 Marks)
Ans: Indirect method to convert decimals to octal is by first converting the decimal number to another number system like binary or hexadecimal, then converting into binary from hexadecimal and using the grouping from the octal numbers.
For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates
Check-Out:
Comments