How Decimal Place Value Works
The position of each digit in a decimal number tells you its value. This is called place value.
The first place to the right of the decimal point is tenths (÷ 10). The second is hundredths (÷ 100). The third is thousandths (÷ 1000). So in the decimal 3.756:
- The 3 is three whole units
- The 7 is seven tenths (0.7)
- The 5 is five hundredths (0.05)
- The 6 is six thousandths (0.006)
Added together: 3 + 0.7 + 0.05 + 0.006 = 3.756.
Decimals and fractions
Every decimal can be written as a fraction. The decimal 0.5 is the same as ½. The decimal 0.25 is the same as ¼. The decimal 0.1 is the same as 1/10. Decimals and fractions are two ways of expressing the same idea — parts of a whole.
Working With Decimals
Adding and subtracting decimals works exactly like adding whole numbers — as long as you line up the decimal points.
``
3.75
+ 1.40
------
5.15
``
(Tip: add a zero to 1.4 to make the columns line up.)
Multiplying decimals
To multiply decimals, ignore the decimal point first. Multiply as if they are whole numbers. Then count the total number of decimal places in both numbers and place the decimal point that many places from the right in your answer.
Example: 2.3 × 1.4 → multiply 23 × 14 = 322 → two decimal places total → answer is 3.22.
Dividing decimals
The easiest method is to convert the divisor to a whole number. Multiply both numbers by 10, 100, or 1000 until the number you are dividing by has no decimal. Then divide as normal.
Example: 4.8 ÷ 0.4 → multiply both by 10 → 48 ÷ 4 = 12.
Decimals in Everyday Life
Decimals appear everywhere once you know what to look for. Prices always involve decimals — £4.99 means 4 pounds and 99 hundredths of a pound. Measurements use decimals constantly: your height, the weight of ingredients in a recipe, the speed of a car in km/h.
Decimals in science and data
Scientists use decimals to record precise measurements. A temperature of 36.8°C is more useful than saying 'about 37°C'. Rainfall is measured to one decimal place. A runner's time might be recorded to the hundredth of a second.
Rounding decimals
Sometimes a full decimal is more precise than needed. Rounding makes a decimal simpler. To round to one decimal place, look at the second decimal digit. If it is 5 or more, round up. If it is 4 or less, round down. So 3.47 rounded to one decimal place is 3.5. And 3.44 rounds to 3.4.
The same rule applies when rounding to any number of decimal places. Fractions and decimals work together throughout maths and science.
Frequently asked questions
- What is the difference between a decimal and a fraction?
- Both represent parts of a whole, just in different notation. A fraction writes the parts over the total (¾), while a decimal uses place value to the right of a point (0.75). They mean the same thing and can be converted between each other. Decimals are often easier for calculations, while fractions show exact ratios more clearly.
- Why do some decimals go on forever?
- When you convert a fraction to a decimal, some fractions produce a pattern that never ends. The fraction ⅓ becomes 0.333... repeating forever. The fraction 1/7 creates a six-digit repeating pattern: 0.142857142857... These are called recurring decimals. Others, like pi (3.14159...), never repeat and never end.
- How do you compare two decimals to see which is bigger?
- Compare place by place, starting from the left. First compare the whole-number part. If equal, compare the tenths digit. If still equal, compare the hundredths digit. So 3.45 is greater than 3.39 because in the tenths column, 4 is greater than 3. Never judge by the number of digits alone — 0.9 is larger than 0.89.
- What is a terminating decimal?
- A terminating decimal has a finite number of digits after the decimal point — it ends. For example, 0.25, 0.5, and 0.125 all terminate. A decimal terminates when the denominator of the equivalent fraction has only the prime factors 2 and 5. Fractions like ⅓ or ⅙ produce non-terminating, recurring decimals.