Decimals

A decimal is a way to write numbers that are between whole numbers, using a dot called a decimal point.

Reading is good — doing is better. Practice Decimals as an interactive lesson.

Definition

A decimal number has two parts separated by a decimal point (.). The digits to the left of the dot are whole numbers. The digits to the right of the dot are parts of a whole — tenths, hundredths, thousandths, and so on. For example, 3.47 means 3 wholes plus 4 tenths plus 7 hundredths.

Remember the rule

Line up the decimal points when adding or subtracting decimals. Compare decimals place by place from left to right — the first place where the digits differ tells you which number is bigger.

Key words

Decimal point: The dot (.) that separates the whole number part from the fraction part of a number.
Tenths: The first place to the right of the decimal point. One tenth means 1 out of 10 equal parts (0.1).
Hundredths: The second place to the right of the decimal point. One hundredth means 1 out of 100 equal parts (0.01).
Thousandths: The third place to the right of the decimal point. One thousandth means 1 out of 1,000 equal parts (0.001).
Place value: The value of a digit based on where it sits in the number. In 4.73, the 7 is in the tenths place, so it means 7 tenths.
Equivalent decimals: Decimals that have the same value even if they look different. For example, 0.5 and 0.50 are equal.
Rounding: Changing a decimal to a nearby, simpler number. For example, 3.47 rounded to the nearest tenth is 3.5.
Comparing decimals: Deciding which decimal is greater or less by looking at each place value from left to right.

Worked examples

Write 0.6 in words and as a fraction.

→ Zero and six tenths. As a fraction: 6/10. · The tenths place is the first digit right of the decimal point.

Add 2.4 + 1.35

→ Line up the decimal points: 2.40 + 1.35 = 3.75 · Writing 2.4 as 2.40 makes it easier to line up and add each place.

Subtract 5.6 − 2.83

→ Write 5.6 as 5.60. Then 5.60 − 2.83 = 2.77

Which is greater, 0.4 or 0.38?

→ 0.4 is greater. In the tenths place, 4 is bigger than 3, so 0.4 > 0.38. · Many kids think 0.38 is bigger because 38 looks larger than 4 — but you must compare place by place.

Round 6.752 to the nearest hundredth.

→ Look at the thousandths digit: it is 2. Since 2 is less than 5, round down. Answer: 6.75

Multiply 0.3 × 4

→ Think of it as 3 tenths × 4 = 12 tenths = 1.2 · Count the decimal places in the factors (one here) and put the same number in the answer.

Common mistakes

Thinking 0.38 is greater than 0.4 because 38 is greater than 4 — always compare digit by digit starting at the tenths place.
Forgetting to line up the decimal points when adding or subtracting, which scrambles the place values.
Dropping the zero placeholder, such as writing .5 instead of 0.5, which can cause confusion about the value.
Moving the decimal point the wrong number of places when multiplying or dividing by 10, 100, or 1,000.
Thinking that more decimal digits always means a bigger number — 0.900 is less than 1.0 even though it has more digits.

FAQs

Why do we need decimals if we already have fractions?

Decimals are just another way to write fractions, but they are much easier to add, subtract, and compare because they use the same place-value system as whole numbers. Money, measurements, and most calculators use decimals.

Is 0.5 the same as 1/2?

Yes! 0.5 means 5 tenths, which equals 5/10, and 5/10 simplifies to 1/2. They are exactly the same value.

Why do we add zeros after a decimal, like writing 2.4 as 2.40?

Adding a zero at the end of a decimal does not change its value — 2.4 and 2.40 are equal. We do it to make place values line up neatly when adding or subtracting.

How do I multiply a decimal by 10?

Move the decimal point one place to the right. For example, 3.56 × 10 = 35.6. Multiply by 100 and move it two places right: 3.56 × 100 = 356.

What is the difference between 0.1 and 0.01?

0.1 is one tenth and 0.01 is one hundredth. One tenth is ten times larger than one hundredth. Think of a dollar: 0.1 of a dollar is 10 cents, and 0.01 of a dollar is 1 cent.

How do I round a decimal to the nearest tenth?

Look at the hundredths digit (the second digit after the decimal point). If it is 5 or more, round the tenths digit up by 1. If it is 4 or less, keep the tenths digit the same and drop the rest. Example: 4.67 rounds to 4.7 because the hundredths digit is 7.

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