Place Value
Solve problems involving multiplying or dividing natural numbers by multiples and powers of 10, using the place value of digits. Note: whole-number place value itself is completed by Year 3.
Read this first
Where a digit sits tells you what it is worth. The 3 in 3000 is worth a lot more than the 3 in 30.
Read it as four thousand, two hundred and seventy-five.
Words you need
- Digit
- One number symbol. There are ten of them: 0 to 9.
- Place value
- What a digit is worth, based on where it sits.
- Column
- Each spot a digit can sit in. Ones, tens, hundreds, thousands.
Worked example
e.g. What is the 7 worth in 4275?
- Put the number in columns.
- Find the 7. It sits in the tens column.
- One ten is 10. So seven tens is 70.
- The 7 is worth 70.
Always find the column first. The column tells you the answer.
Practice
The pictures fade as you go. By the last few you are on your own.
1What is the 8 worth in 3856?with a picture
Answer800. The 8 sits in the hundreds column, so it is worth 8 hundreds.
2What is the 2 worth in 2149?with a picture
Answer2000. The 2 sits in the thousands column.
3What is the 5 worth in 6503?with a hint
Need a hint?
Count the columns from the right: ones, tens, hundreds.
Answer500. The 5 is in the hundreds column.
4Write four thousand and sixty as a number.with a hint
Need a hint?
There are no hundreds. Put a 0 there to hold the space.
Answer4060. The 0 in the hundreds column holds the space so the 4 stays in the thousands.
5What is the 9 worth in 9412?on your own
Answer9000.
6Which is bigger: 3450 or 3540?on your own
Answer3540. Both have 3 thousands. Then compare hundreds: 5 beats 4.
7Write 7000 + 200 + 30 + 6 as one number.on your own
Answer7236.
Think about it
1
Why is the 0 in 4060 important?
One good answerIt holds the hundreds space. Without it you would write 466, and the 4 would slip into the hundreds column. Zero keeps the other digits in the right place.
2
The same digit 5 is in 5000 and in 50. Is it worth the same?
One good answerNo. In 5000 it is worth five thousand. In 50 it is worth fifty. The digit is the same, but the column is different, so the value is different.
3
How do you compare two big numbers quickly?
One good answerStart at the biggest column on the left. If they match, move one column right. The first column that differs decides it.
Common mistakes
Saying the 7 in 4275 is worth 7.
Look at the column. The 7 is in the tens, so it is worth 70, not 7.
Leaving out a zero, like writing 46 for four thousand and sixty.
Every empty column needs a 0. The zero holds the space.
Thinking a longer number is always bigger.
That is true for whole numbers, but only if you count the digits properly. 999 has 3 digits and 1000 has 4, so 1000 wins.