Understanding place value
🎯 In this topic you will
- Read and write whole numbers greater than 1000.
- Explain the value of each digit in a whole number and how its position affects that value.
- Multiply and divide whole numbers by 10 and 100, and describe how the digits move.
- Compose (put together) and decompose (split) whole numbers.
🧠 Key Words
- compose
- decompose
- equivalent
- hundred thousand
- million
- place holder
- regroup
- ten thousand
- thousand
Show Definitions
- compose: To put numbers together to make a larger number.
- decompose: To break a number into smaller parts based on place value.
- equivalent: Having the same value even if written in a different way.
- hundred thousand: A place value equal to 100,000, which is ten times greater than ten thousand.
- million: A number equal to 1,000,000, made up of one thousand thousands.
- place holder: A zero used in a number to keep digits in the correct place value.
- regroup: To exchange values between place values when adding or subtracting.
- ten thousand: A place value equal to 10,000, which is ten times greater than one thousand.
- thousand: A place value equal to 1,000.
Working with Larger Numbers
I n this section, you will work with bigger numbers, including thousands, ten thousands, and hundred thousands. You will also multiply and divide whole numbers by 10 and 100.
❓ EXERCISES
1. What is the value of the digits in $950\,302$?
a. What is the value of the digit $9$?
b. What is the value of the digit $5$?
👀 Show answer
a. The digit $9$ is in the hundred thousands place, so its value is $900\,000$.
b. The digit $5$ is in the ten thousands place, so its value is $50\,000$.
2. Mia is thinking of a $5$-digit whole number.
She says, ‘It has a $2$ in the ten thousands place and in the tens place.
It has a $5$ in the thousands place and in the ones place.
It has a $0$ in the hundreds place.’
What number is Mia thinking of?
Write your number in words.
👀 Show answer
The number is $25\,025$.
In words: twenty-five thousand and twenty-five.
3. Decompose these numbers by copying and filling in the missing numbers.
a. $805\,469 = 800\,000 + 5\,000 + 400 + 60 + 9$
b. $689\,567 = 600\,000 + 80\,000 + 9\,000 + 500 + 60 + 7$
c. $508\,208 = 500\,000 + 8\,000 + 200 + 8$
👀 Show answer
Each number has been split into the value of its digits using place value.
4. Bruno says, ‘The largest $5$-digit number is $1$ less than a hundred thousand.’
Is Bruno correct? Explain your answer.
👀 Show answer
Yes. The largest $5$-digit number is $99\,999$, which is $1$ less than $100\,000$.
5. Which number sentence has a different missing number? What is it?
$\square \times 100 = 30\,000$
$3 \times 100 = \square$
$30\,000 \div 100 = \square$
$\square \div 10 = 30$
$\square \times 100 = 3\,000$
$\square \times 10 = 3\,000$
👀 Show answer
The different missing number is in $\square \times 10 = 3\,000$, where the missing number is $300$.
6. Calculate:
a. $67 \times 10$
b. $40 \div 10$
c. $3\,600 \div 100$
d. $415 \times 10$
e. $350 \div 10$
f. $35 \times 100$
👀 Show answer
a. $670$
b. $4$
c. $36$
d. $4\,150$
e. $35$
f. $3\,500$
7. If you multiply $606$ by $10$, what changes and what stays the same?
Discuss your answer with your partner.
👀 Show answer
The digits stay the same, but each digit moves one place to the left. The value becomes $6\,060$.
🧠 Think like a Mathematician
Digital sum
The digits in the number $15$ total $6$ ($1 + 5 = 6$).
a. Find all the whole numbers that have digits with a total of $6$. Do not include zero in any of your numbers.
b. What is the largest number?
c. What is the smallest number?
You will show you are specialising when you find whole numbers that have digits with a total of $6$.
👀 show answer
- a. Examples include $6$, $15$, $24$, $33$, $114$, $123$, $222$, and many others, as long as the digits add to $6$ and no digit is zero.
- b. There is no single largest number, because you can always make a larger number by adding more digits that still total $6$, such as $111111$.
- c. The smallest number is $6$.
💡 Quick Math Tip
Digital sum pattern: When finding numbers with a given digital sum, focus on how the digits add together, not on how many digits the number has. You can make many different numbers with the same total by rearranging or splitting the digits, as long as their sum stays the same and zero is not used.