Place value, step by step
Numbers up to a billion: millions, thousands and ones, and the value of every digit. Read one step, play with it, then tap “I understand this”.
Every digit has a place
In Grade 7 you work with numbers up to 1 000 000 000. Every digit sits in a column: millions, thousands and ones, each group in hundreds, tens and ones.
10 of one place make 1 of the place to its left: 10 ones = 1 ten, 10 tens = 1 hundred, and so on.
Build a number
Change the digit in each column. The words and the expanded notation change too.
Big numbers get a space after every three digits from the right: we write 284 056 731. It makes them easier to read.
When you have 10 ones, you bundle them into 1 ten, and 10 tens into 1 hundred. That is how just ten digits (0 to 9) can write any number, however big. The place of a digit tells you how many bundles it stands for.
The value of a digit
The same digit is worth more when it sits further left: every place to the left is worth ten times more.
Value = digit × its place.
What is the digit worth?
Choose the value of the bold digit.
Correct: 0Expanded notation
Expanded notation breaks a number up into the value of each digit:
284 056 731 = 200 000 000 + 80 000 000 + 4 000 000 + 50 000 + 6 000 + 700 + 30 + 1
If a digit is 0, we leave it out: 30 200 450 = 30 000 000 + 200 000 + 400 + 50.
What is missing?
Choose the part that goes in the box.
Correct: 0The 0 holds a place open. Without the 0 in 5 038, the 3 moves into the hundreds and you get 538: a completely different number.
Number names in words
Read the number in groups of three, from the left: 284 056 731 is two hundred and eighty-four million fifty-six thousand seven hundred and thirty-one.
Watch the zeros. “three million and twenty” is 3 000 020, not 320 or 30 020. Every place needs a digit.
Which number is it?
Read the words and choose the right number.
Correct: 0Compare and order
To compare two numbers, start on the left. The first place where the digits differ decides.
284 065 731 > 284 056 731
Order them
Tap the numbers from the smallest to the biggest.
The digit on the far left is worth the most. One thousand is more than all the hundreds, tens and ones together (999), so the left side decides first.
More and less
When you add 10, 100 or 1 000, only one digit changes, unless it goes past a 9.
Jump with the number
Tap a button and watch which column changes.
Check yourself
- Every place is worth 10 times more than the place to its right.
- Value = digit × its place. In 4 762 the 7 is worth 700.
- A 0 holds a place open: 5 038 is not 538.
- Compare from the left: the first digit that differs decides.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 1 A4 pagePractice sheet
- Numbers9 pages · PDFPaperMemo
Ready for more? The Grade 7 place value quiz gives you new numbers every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Use money: R762 is 7 R100 notes, 6 R10 notes and 2 R1 coins. Children grasp place value quickly with money.
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 7 Maths. Always check your teacher’s notes and textbook too.