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A digit's worth depends entirely on where it sits. This guide walks you through place value, decimals, multiplying and dividing by powers of 10, rounding to decimal places and significant figures, and estimating to check that your answers make sense.
Mapped to the Cambridge Lower Secondary Mathematics curriculum framework.
A digit's value depends on the column it sits in. Each column is ten times the next.
Place value is the idea that where a digit sits changes its value. In 3 472, the 4 is worth 400, but in 3 274 the same digit 4 is worth only 40.
Reading the chart left to right gives the parts: .
The pattern of place value carries on past the decimal point — into tenths, hundredths and thousandths.
The decimal point does not stop place value — it just continues the pattern. The columns after the point are tenths, hundredths and thousandths, each still ten times smaller than the one before.
So means .
Multiplying or dividing by 10, 100 or 1000 simply shifts every digit.
Because each place is ten times the one to its right, multiplying or dividing by powers of 10 just shifts the digits. The decimal point stays put — it is the digits that move.
Rounding keeps numbers tidy. Check the next digit to decide up or down.
Rounding keeps numbers tidy and useful. To round to a number of decimal places, look at the next digit — the first one you are about to drop.
So rounded to 1 decimal place is — the next digit, 7, rounds the 4 up to 5. Rounded to 2 decimal places it is — the next digit, 1, rounds down.
Significant figures count the digits that carry the real weight, starting from the first non-zero digit.
Significant figures are the digits that carry the real information in a number. You start counting from the first non-zero digit.
In , the first significant figure is the 3, the second is the 4, and so on. In , the leading zeros are just placeholders — the first significant figure is the 6.
To round to a number of significant figures, find the last digit you want to keep, then use the next digit and the same up/down rule as before.
Round the numbers first to get a quick, rough answer you can trust.
An estimate is a rough answer you work out quickly by rounding the numbers first — usually to 1 significant figure. It is one of the most powerful checking tools in maths.
Suppose a calculator gives . Is that sensible? Round each number: and . Then . The estimate is close to 5928, so the answer looks right.
Place value and rounding support measurement, money and data work everywhere.
Getting confident with place value and rounding now makes lots of later topics easier:
If a topic later feels hard, it is often a place-value step underneath that needs a quick refresh. Come back to this guide whenever you need it — there is no prize for rushing.
Sources: Cambridge Lower Secondary Mathematics curriculum framework (Stage 7). Last reviewed 2026-05-19.
Step-by-step solutions for place value and rounding, written exactly the way a tutor would explain them at the board.
Question
In the number 58 304, what is the value of the digit 8?
Step-by-step solution
Step 1
Find the column the 8 sits in, working from the right: ones, tens, hundreds, thousands.
Step 2
The 8 is in the thousands column.
Step 3
So its value is 8 thousands.
Answer
The digit 8 is worth .
Question
Work out .
Step-by-step solution
Step 1
has two zeros, so every digit shifts two places to the left.
Question
Round to 1 decimal place.
Step-by-step solution
Step 1
1 decimal place means keeping one digit after the point — the 6.
Step 2
Look at the next digit, the 8. It is 5 or more, so round up.
Step 3
Round the 6 up to 7.
Question
Round to 2 significant figures.
Step-by-step solution
Step 1
The first significant figure is the 4, the second is the 6. Keep both.
Step 2
Look at the next digit, the 7. It is 5 or more, so round up.
Step 3
Round the 6 up to 7, and use zeros to hold the place value.
Question
A calculator shows . Use an estimate to decide whether this is sensible, then explain.
Step-by-step solution
Step 1
The important words for place value and rounding and what they mean — learn these so you can explain your thinking clearly.
The value of a digit based on its position in a number. Each place is ten times the place to its right.
Any of the symbols 0 to 9 used to write numbers. The number 472 is made of the digits 4, 7 and 2.
A number that uses a decimal point to show parts smaller than one, such as tenths and hundredths.
Example
is a decimal with 2 tenths and 7 hundredths.
The dot that separates the whole-number part of a number from the part smaller than one.
A number made by multiplying 10 by itself, such as 10, 100 and 1000. Multiplying or dividing by one of these shifts every digit.
Example
and are powers of 10.
Replacing a number with a nearby simpler value to a chosen level of accuracy.
The position of a digit after the decimal point. Rounding to 2 decimal places keeps two digits after the point.
Example
has 2 decimal places.
A digit that carries meaning about the size of a number, counted from the first non-zero digit.
Example
has 2 significant figures when rounded from .
A rough answer found quickly by rounding the numbers in a calculation, used to check that an answer is sensible.
Close to in value but not exact. Written with the symbol .
Example
when rounded to 1 significant figure.
The first column after the decimal point — each unit there is one tenth, or .
Example
In , the digit 2 stands for 2 tenths.
A zero at the start of a decimal that holds the place value but is not a significant figure.
Example
In the zeros before the 6 are leading zeros.
The slip-ups students most often make with place value and rounding — and simple ways to avoid them.
Why it happens
The 'add a zero' shortcut is learned for whole numbers and then used on decimals.
How to avoid it
Shift the digits one place left instead: . The zeros trick only works for whole numbers.
Why it happens
A longer string of digits looks like a bigger number.
How to avoid it
Give the decimals the same number of places first: versus shows is larger.
Why it happens
Each digit is rounded one at a time instead of in a single decision.
How to avoid it
Round once, using only the next digit. to 1 decimal place is .
Why it happens
Every digit is counted, including the place-holding zeros.
How to avoid it
Start counting from the first non-zero digit. has 2 significant figures.
Why it happens
When rounding up makes a 9 into 10, the carry into the next column is missed.
How to avoid it
Carry the 1: rounds to . Keep the trailing zero to show the accuracy.
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Each column is ten times the one to its right. That single fact is what lets you compare numbers: to decide which of two whole numbers is bigger, line them up by their columns and compare from the left. The first column where they differ decides it.
A useful tip: writing extra zeros on the end of a decimal does not change its value, because the new columns are empty. So . This makes comparing decimals easier — give them the same number of decimal places, then compare digit by digit. To compare and , rewrite as ; now you can see is larger.
The number of zeros tells you how many places to shift. For , shift three places: .
If you run out of digits, fill the gap with zeros. , and .
One thing to watch: when rounding up causes a 9 to become 10, you carry. to 1 decimal place is , not . Keep the trailing zero — it shows the level of accuracy.
Significant figures are handy because they keep the size of a number while trimming the detail — useful for sensible, easy-to-read estimates.
Now imagine you had pressed a wrong key and got 59 280. The estimate of 6000 is nowhere near, so you would know to try again.
The same trick works for division. To check , round to .
Always estimate before trusting a calculator answer, not after. The symbol means "is approximately equal to" — use it whenever you round for an estimate.
Step 2
Shifting two places left gives 360 (fill the empty column with a zero).
Answer
Answer
Answer
Round each number to 1 significant figure.
Step 2
Multiply the rounded numbers for an estimate.
Step 3
The estimate is very close to the calculator's .
Step 4
Because the two values are close, the calculator answer looks sensible.
Answer
The estimate is , which is close to , so the answer is sensible.