Place Value and Rounding
The position of a digit decides its value, and rounding trims numbers to a chosen place.
About this topic
Place value is the idea that a digit's worth depends on where it sits. In 3,476 the 4 means four hundreds, not just four, because each place is ten times larger than the one to its right. This base-ten structure is what makes column addition, long multiplication and decimals work.
We can write 3,476 in expanded form as 3 × 1000 + 4 × 100 + 7 × 10 + 6 × 1. The zero is a placeholder that keeps other digits in their correct places: 305 and 35 are very different numbers because of the zero. Moving right past the decimal point the places become tenths, hundredths and thousandths, each ten times smaller.
Rounding replaces a number with a nearby, simpler one. Look at the digit just right of the place you are rounding to: 5 or more rounds up, 4 or less keeps the digit. To round 3,476 to the nearest hundred, look at the 7 in the tens place. It is 5 or more, so the 4 goes up and the answer is 3,500. Rounding is the key tool for quick estimates and for checking whether an exact answer is sensible, for example when you estimate a restaurant bill or a shopping total.
A common mistake is looking at every digit to the right instead of only the one next door. Rounding 2,449 to the nearest hundred gives 2,400, not 2,500, because only the 4 in the tens place matters. Also remember that rounding is an approximation, so rounded answers should use the symbol for approximately equal.
Key ideas
- Each place is ten times the one to its right
- Round up when the next digit is 5 or more
- Rounding gives a close estimate that is easier to use
Quick check
Use cases: where Place Value and Rounding helps
- Homework: review the key idea behind Place Value and Rounding before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Place Value and Rounding without notes.
- Visual learning: play with the interactive lab to see how Place Value and Rounding changes when you adjust its inputs.
- Teaching a friend: explain Place Value and Rounding in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Place Value and Rounding?
The position of a digit decides its value, and rounding trims numbers to a chosen place.
What will I learn in Place Value and Rounding?
Each place is ten times the one to its right. Round up when the next digit is 5 or more. Rounding gives a close estimate that is easier to use.
Is Place Value and Rounding part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Place Value and Rounding lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Place Value and Rounding?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.