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Learn Decimals

Tenths, hundredths and the place-value rules that make them easy.

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Decimals extend place value to the right of the ones place: tenths, hundredths, thousandths and beyond. 3.47 means 3 ones, 4 tenths and 7 hundredths. They are how we write money, measurements and most data, so they matter well beyond school. The main skills are reading place value, comparing and rounding, the four operations, and converting between decimals, fractions and percents. Most mistakes come from treating the digits after the point like a whole number, for instance thinking 0.25 is bigger than 0.3. Learnr builds a decimals course for your level, for a student, an adult or a parent helping a child, and teaches it in short interactive lessons.

How to learn Decimals, step by step

Tie decimals to money and measurement. Use dollars and cents: $0.30 is 30 cents and $0.25 is 25 cents, so 0.3 is bigger than 0.25. Rulers marked in tenths of a centimeter work well too.
Compare by filling in zeros. To compare 0.3 and 0.25, rewrite 0.3 as 0.30. Now both have hundredths, and 30 hundredths is clearly more than 25. Then practice ordering a list of five decimals.
Line up the points to add and subtract. Stack 12.5 and 3.75 with the decimal points in one column, add a zero to make 12.50, then add as usual for 16.25. The point in the answer stays in the same column.
Multiply first, then count decimal places. For 0.3 times 0.2, multiply 3 by 2 to get 6, then count two decimal places in total, giving 0.06. Estimate first so a misplaced point is obvious.
Make the divisor a whole number. For 1.5 divided by 0.3, move both decimal points one place right to get 15 divided by 3, which is 5. Moving both points by the same amount keeps the answer unchanged.
Connect decimals to fractions with daily practice. Learn the common pairs: 0.5 is 1/2, 0.25 is 1/4, 0.2 is 1/5 and 0.125 is 1/8. A short daily Learnr lesson with a streak keeps these conversions quick.

What you'll learn

Read and write decimals using place value names
Compare, order and round decimals correctly
Add and subtract decimals by lining up the decimal points
Multiply and divide decimals, including dividing by a decimal
Convert between decimals, fractions and percents

What's inside your Decimals course

A sample path Learnr builds for Decimals. Your real course adapts to your goal and level.

1. Tenths, hundredths and place value
2. Comparing, ordering and rounding
3. Adding and subtracting decimals
4. Multiplying decimals
5. Dividing decimals
6. Decimals, fractions and percents together

How long does it take to learn Decimals?

Students usually learn decimal place value, comparing and adding over a few weeks, and decimal multiplication and division over a few more, roughly 4 to 8 weeks of regular practice in total. Adults reviewing can often finish in 1 to 3 weeks.

What you need before you start

Whole-number place value, the four operations with whole numbers, including long division, and a basic understanding of fractions like tenths and hundredths.

Common mistakes to avoid

Thinking longer decimals are bigger, as if 0.125 beats 0.5 because 125 is more than 5. Compare place by place starting at the tenths.
Lining up the last digits instead of the decimal points when adding, so 12.5 plus 3.75 gets added as if it were 125 plus 375.
Expecting multiplication to always make a number bigger. Multiplying by a decimal less than 1, like 0.5, makes it smaller.

How Learnr builds your course

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Decimals questions, answered

How do I help my child understand decimals?

Start with money, since children already know 50 cents is half a dollar. Use base-ten blocks or a 10 by 10 grid to show tenths and hundredths, and compare decimals using prices in stores.

Why does 0.1 times 0.1 equal 0.01?

One tenth of one tenth is one hundredth. On a 10 by 10 grid, a tenth of a tenth is just one small square out of 100.