Number System
Grade 6 Math Worksheets
A number system is a systematic way of representing and expressing numbers. Different cultures and applications have developed various number systems throughout history, but some of the most commonly used systems include:
Decimal Number System (Base-10)
This is the most common number system used in everyday life. It uses the digits 0 through 9 to represent numbers. Each digit’s place value is a power of 10. For example, in the number 245, the digit 5 is in the units place, 4 is in the tens place (10^1), and 2 is in the hundreds place (10^2).
Binary Number System (Base-2)
Computers use the binary system, which only uses the digits 0 and 1. Each digit’s place value is a power of 2. Binary is fundamental to computer science and digital electronics.
Octal Number System (Base-8)
This system uses the digits 0 through 7. Each digit’s place value is a power of 8. Octal is less common today but has historical significance in computing.
Hexadecimal Number System (Base-16)
This system uses the digits 0-9 and the letters A-F to represent values from 0 to 15. Each digit’s place value is a power of 16. Hexadecimal is commonly used in computing, especially in programming and representing memory addresses.
Roman Numerals
This ancient system uses combinations of letters (I, V, X, L, C, D, M) to represent numbers. For example, I is 1, V is 5, X is 10, and so on. The system is additive, meaning values are added together, but there are also subtractive combinations (e.g., IV for 4).
Ternary Number System (Base-3)
This system uses the digits 0, 1, and 2. Each digit’s place value is a power of 3. While less common than binary or decimal, it’s sometimes used in mathematical and computer science contexts.
Complex Number System
This system represents numbers in the form a + bi, where “a” and “b” are real numbers, and “i” is the imaginary unit (i.e., the square root of -1). Complex numbers are used in various branches of mathematics and engineering.
Personalized Online Tutoring
Number System - Grade 6 Math Worksheet PDF
This is a free printable / downloadable PDF worksheet with practice problems and answers. You can also work on it online.
Sign up with your email ID to access this free worksheet.
"We really love eTutorWorld!"
"We really love etutorworld!. Anand S and Pooja are excellent math teachers and are quick to respond with requests to tutor on any math topic!" - Kieran Y (via TrustSpot.io)
"My daughter gets distracted easily"
"My daughter gets distracted very easily and Ms. Medini and other teachers were patient with her and redirected her back to the courses.
With the help of Etutorworld, my daughter has been now selected in the Gifted and Talented Program for the school district"
- Nivea Sharma (via TrustSpot.io)
Different number systems are suitable for different applications. For instance, binary is well-suited for computer operations, while decimal is convenient for everyday calculations. Understanding these systems is essential in various fields, including mathematics, computer science, and engineering.
The number system can best be demonstrated by the following diagram:
![Number System Number System](https://www.etutorworld.com/wp-content/uploads/2024/06/Number-System.jpeg)
“There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.
Our kid is doing much better with a higher score.”
6th Grade Tutoring
eTutorWorld offers Personalized Online Tutoring for Math, Science, English, and Standardised Tests.
Our Tutoring Packs start at just under $22.49 per hour, and come with a moneyback guarantee.
Schedule a FREE Trial Session, and experience quality tutoring for yourself. (No credit card required.)
Solved Examples
Adding soon…
Do You Stack Up Against the Best?
If you have 30 minutes, try our free diagnostics test and assess your skills.
Frequently Asked Questions
What is a number system?
A number system is a way of expressing numbers using digits or symbols. It consists of a set of rules for representing numerical values and performing arithmetic operations.
How are number systems classified?
Number systems are classified based on the base or radix they use. Common classifications include binary (base-2), octal (base-8), decimal (base-10), and hexadecimal (base-16) systems.
What is the binary number system?
The binary number system uses only two digits, 0 and 1. It is widely used in computers and digital systems, where information is represented using binary code.
Why is the decimal system called base-10?
The decimal system is called base-10 because it uses ten digits (0 through 9) to represent numbers. Each place value in a decimal number is a power of 10.
How does the octal number system work?
The octal system is base-8 and uses the digits 0 through 7. It is often used in computing and programming, especially when dealing with binary-coded values.
What are hexadecimal numbers used for?
Hexadecimal (base-16) numbers use digits 0-9 and the letters A-F to represent values. They are commonly used in computing to represent binary-coded values more compactly.
How do you convert a decimal number to binary?
To convert a decimal number to binary, repeatedly divide the decimal number by 2 and note the remainders. The binary equivalent is the sequence of remainders read in reverse order.
What is the significance of the place value in number systems?
Place value indicates the position of a digit within a number and its contribution to the overall value. The rightmost digit represents the units place, the next digit to the left is the tens place, and so on.
Can you perform arithmetic operations across different number systems?
Yes, arithmetic operations can be performed across different number systems. However, conversion to a common base is often necessary before performing operations.
How are negative numbers represented in different number systems?
Negative numbers can be represented using various methods, such as signed magnitude, two’s complement (commonly used in binary systems), or other specialized representations depending on the base of the number system.
![](https://www.etutorworld.com/wp-content/uploads/2023/04/Gloria-150x150-2-150x150.webp)
Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn
Affordable Tutoring Now Starts at Just $22.49
eTutorWorld offers affordable one-on-one live tutoring over the web for Grades K-12. We are also a leading provider of Test Prep help for Standardized Tests (SCAT, CogAT, MAP, SSAT, SAT, ACT, ISEE, and AP).
What makes eTutorWorld stand apart are: flexibility in lesson scheduling, quality of hand-picked tutors, assignment of tutors based on academic counseling and diagnostic tests of each student, and our 100% money-back guarantee.
Whether you have never tried personalized online tutoring before or are looking for better tutors and flexibility at an affordable price point, schedule a FREE TRIAL Session with us today.
*There is no purchase obligation or credit card requirement
Grade 6 Science Worksheets
- Inquiry process
- Nature of Science
- Scientific Inquiry
- Inquiry, Analysis and Problem Solving
- Ethical Practices
- Science and Society
- Biotic and Abiotic Factors
- Impact of Organisms
- Adaptation
- Spheres of Earth
- Natural Resources
- Environmental Issues
- Conservation of Earth
- Understanding Technology
- Abilities To Do Technological Design
- Structure of Earth
- Solar System
- Rocks and Fossils
- Earth Systems
- Plate Tectonics
- Evolution
- Magnetic Field of Earth
- Geologic Time
- Materials and Processes That Shape a Planet
- Astronomy
- Ecology
- Energy
- Kinetic and Potential Energy
- Energy Transfer
- Matter and its Structure
- States of Matter
- Physical and Chemical Changes
- Force and Motion
- Electricity and Magnetism
- Wave Interactions
- Sound
- Light
- Introduction to Life Science
- The Origin & History of Life On Earth
- Plant and Animal Cells
- Parts of a Cell
- The Cell Cycle
- How Living Organisms Get Energy
- Classification of Organisms
- How Plants Grow & Reproduce
- The Human Respiratory System
- The Human Cardiovascular System
- The Human Digestive System
- The Human Endocrine Systems
- The Human Nervous System
- The Human Muscular System
- The Human Skeletal System
IN THE NEWS
![Logo-eTutorWorld-wordmark-white](https://www.etutorworld.com/wp-content/uploads/2020/07/Logo-eTutorWorld-wordmark-white.png)
Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.
Online test prep and practice
SCAT
SSAT
ISEE
PSAT
SAT
ACT
AP Exam
Science Tutoring
Physics Tutoring
Chemistry Tutoring
Biology Tutoring
Math Tutoring
Pre-Algebra Tutoring
Algebra Tutoring
Pre Calculus Tutoring
Calculus Tutoring
Geometry Tutoring
Trigonometry Tutoring
Statistics Tutoring
Quick links
Free Worksheets
Fact sheet
Sales Partner Opportunities
Parents
Passive Fundraising
Virtual Fundraising
Our Expert Tutors
Safe and Secure Tutoring
Interactive Online Tutoring
After School Tutoring
Elementary School Tutoring
Middle School Tutoring
High School Tutoring
Home Work Help
Math Tutors New York City
Press
©2022 eTutorWorld Terms of use Privacy Policy Site by Little Red Bird
©2022 eTutorWorld
Terms of use
Privacy Policy
Site by Little Red Bird