Decimals
Decimals extend place value to the right of the point using tenths, hundredths and more.
About this topic
Decimals extend place value to the right of the decimal point, with places for tenths, hundredths, thousandths and so on. They are just fractions with denominators that are powers of ten, so 0.75 is 75/100 or 3/4.
Line up the decimal points when adding or subtracting. When multiplying, ignore the points, multiply, then place the point so that the answer has as many decimal places as the factors combined. For 0.3 × 0.04, 3 × 4 = 12 and there are three decimal places, giving 0.012. Some decimals end, while others repeat forever, like 1/3 = 0.333… To convert a fraction, divide the numerator by the denominator.
Money is the most familiar decimal system: 4.25 dollars is four dollars and twenty-five cents. In sports, race times such as 9.58 seconds are compared by looking at tenths and hundredths. To compare 0.45 and 0.5, pad zeros so that you compare 0.45 and 0.50, and see that 0.5 is bigger.
A common misconception is that a longer decimal is larger, so that 0.123 seems bigger than 0.5. It is not, because tenths matter most. Another is forgetting to line up the decimal points in addition, which gives nonsense. Decimals are used in measurement, science, finance and calculators every day.
Key ideas
- Each place is a tenth of the previous
- Line up decimal points to add
- Fractions convert to decimals by dividing
Quick check
Use cases: where Decimals helps
- Homework: review the key idea behind Decimals before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Decimals without notes.
- Visual learning: play with the interactive lab to see how Decimals changes when you adjust its inputs.
- Teaching a friend: explain Decimals 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 Decimals?
Decimals extend place value to the right of the point using tenths, hundredths and more.
What will I learn in Decimals?
Each place is a tenth of the previous. Line up decimal points to add. Fractions convert to decimals by dividing.
Is Decimals 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 Decimals 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 Decimals?
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.