Maths › Numbers & place value
Numbers & place value
Every number is really a group of digits, and each digit’s value depends on where it sits. Once that idea clicks, rounding, ordering and even negative numbers all turn out to be the same skill, used a few different ways.
What these questions are
These questions check something quieter than hard sums: how carefully you can read a number and picture where each part of it sits. Get comfortable with that one idea, and rounding, ordering and negative numbers stop feeling like separate topics — they’re really the same skill, applied a few different ways.
On this page you’ll cover three things:
- Place value & reading big numbers — what each digit in a number is worth, and turning big numbers into words (and back again).
- Rounding & estimating — rounding to a stated place, and using rounding to check a calculation is roughly right.
- Ordering, comparing & negative numbers — putting numbers in order, including negatives, and reading a number line.
How to crack them
- Read the whole number before you answer — it’s easy to grab the wrong digit if you rush.
- Line up the digits by place: ones, tens, hundreds, thousands, and so on.
- When rounding, look only at the one digit just to the right of the place you’re rounding to.
- On a number line, left is always smaller — even below zero.
A little tip: in every question we’ve bolded the key instruction word — like value, round or smallest — so you always know exactly what you’re being asked to find.
1. Place value & reading big numbers
Every digit in a number has two things about it: what it looks like, and where it sits. The second one is what actually decides its value. Slide a digit one column to the left and its value multiplies by ten; slide it right and its value divides by ten.
A zero doesn’t always mean “nothing”, either. Very often it’s simply holding a column open, so the digits around it stay in the right place.
- Line up the digits by column. 3,047,500 spreads across millions down to ones (sometimes called “units” — they mean the same thing), as in the strip above.
- Find the 4. It isn’t in the thousands or the hundred-thousands column — it sits in the ten-thousands column.
- Turn the column into a value. Ten-thousands means this digit is worth 4 × 10,000.
- Read the whole number too. Three million, forty-seven thousand, five hundred — the two zeros are just holding their columns open.
Your go: place value
Work out the value of the digit, not just what it looks like, then press an answer.
2. Rounding & estimating
Rounding means swapping a number for a nearby, friendlier one — the nearest 10, 100 or 1,000 — so it’s easier to work with. There is one rule for it: look at the single digit just after the place you’re rounding to. Five or more, round up. Less than five, round down.
Estimating simply puts rounding to work: round the numbers in a calculation first, so you can check a real answer is roughly the right size.
Rounding to a stated place
- Find the thousands digit. In 48,637, the thousands column holds an 8.
- Look at the digit just to the right — the hundreds digit. That’s a 6.
- Apply the rule. 6 is 5 or more, so round up: the 8 becomes a 9, and every digit after it becomes zero.
Estimating
- Round each number to a friendly value. 312 rounds to 300; 19 rounds to 20.
- Multiply the rounded numbers. 300 × 20 = 6,000.
- Check it’s sensible. The exact answer is 5,928 — close to 6,000, which shows the estimate is a good one.
Your go: rounding & estimating
Some questions ask you to round to a stated place; others ask for the best estimate.
3. Ordering, comparing & negative numbers
Putting numbers in order just means placing them on an imaginary line and reading them left to right. That works for decimals as well as whole numbers — compare column by column, starting with the biggest place, rather than judging by how many digits a number has.
It works for negative numbers too, as long as you remember one thing: on a number line, left is always smaller, even below zero.
Ordering and comparing
On the number line, −7 sits furthest to the left, so it’s the smallest of the four.
- Picture the number line. Mark roughly where each number sits — the dots above show −7, −3, 0 and 2.
- Read left to right. Furthest left is smallest, furthest right is largest.
- Watch the negatives. −7 looks like a “bigger” number than −3 because 7 is bigger than 3, but for negatives it’s the opposite: −7 is further from zero in the small direction, so it’s smaller.
Negative numbers
From −4°C to 3°C is a rise of 7 degrees — 4 steps up to zero, then 3 more.
- Picture the climb. The temperature starts at −4 and finishes at 3, crossing zero on the way.
- Split the journey at zero. From −4 up to 0 is 4 degrees.
- Add the rest. From 0 up to 3 is another 3 degrees. 4 + 3 = 7.
Your go: ordering & negative numbers
Some questions ask for the smallest or largest; others ask for the difference between two numbers.
That is numbers & place value
This is the foundation the rest of maths sits on, so it’s worth feeling steady here. When you’re ready, head back and try another topic.
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