Whole Numbers — Counting, Ordering and Place Value

In Grade 5 we work with numbers up to 100 000 and beyond. Every digit in a number has a value that depends on its position. This is called place value. Moving one place to the left makes a digit ten times bigger.

We use six columns in our place value table. Each column has its own colour — learn these colours because we use them in every example below:

The number shown is 453 276. Here is what each digit is worth:

• The 4 is in the Hundred Thousands column → its value is 400 000
• The 5 is in the Ten Thousands column → its value is 50 000
• The 3 is in the Thousands column → its value is 3 000
• The 2 is in the Hundreds column → its value is 200
• The 7 is in the Tens column → its value is 70
• The 6 is in the Units column → its value is 6

We can write this in expanded notation — splitting the number to show the value of every digit:

453 276  =  400 000  +  50 000  +  3 000  +  200  +  70  +  6

In Grade 5 we count in larger intervals than Grade 4. An interval is the size of the jump between numbers. Each new number in the pattern is found by adding (counting forwards) or subtracting (counting backwards) the same interval.

We count in these intervals:

To continue a pattern, find the interval first — subtract any term from the one after it. Then keep adding or subtracting that interval to get the next numbers in the pattern.

Large numbers can be shown on a number line. A number line has marked intervals placed at equal distances apart. To place a number that falls between two markers, you estimate its position by working out how far it sits between those two marked intervals.

How to place a number on a number line:

1. Find the two nearest marked intervals on either side of your number.
2. Work out how far your number is from each of those two markers.
3. Mark its estimated position in the right spot between the two markers.

A useful shortcut: if your number is exactly halfway between two markers, place it right in the middle of that gap. The halfway point between two numbers is found by adding them and dividing by 2.

To compare two numbers, always start at the highest place value column and work right, one column at a time, until you find two digits that are different. That is the deciding column. We show the deciding digit in red and equal digits already checked in blue.

Use these symbols to write your answer:

• <  means less than  — the open mouth always faces the bigger number
• >  means greater than
• =  means equal to

To order a list of numbers from smallest to biggest:

Step 1 — Sort by number of digits. Fewer digits = smaller number. A 4-digit number is always smaller than a 5-digit number.

Step 2 — Numbers with the same digit count: compare from the highest column. Find the deciding column to rank them.

A multiple is the result of multiplying a number by any whole number. Multiples are the numbers you say when you count in a times table.

Multiples of 6:

6, 12, 18, 24, 30, 36, …

• A number has infinitely many multiples — the list never ends.
• The first multiple of any number is the number itself (6 × 1 = 6).

A prime number is a number that has exactly 2 factors — 1 and itself. That is all. Nothing else divides into it exactly.

Examples of prime numbers: 2, 3, 5, 7, 11, 13

A composite number has more than 2 factors — other numbers also divide into it exactly.

Examples of composite numbers: 4 (factors: 1, 2, 4)  ·  9 (factors: 1, 3, 9)  ·  15 (factors: 1, 3, 5, 15)

The number 1 is neither prime nor composite. It has only one factor (itself), so it does not fit either definition.

All prime numbers up to 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

💡 2 is the only even prime number. Every other even number has 2 as a factor — which gives it at least 3 factors — so all other even numbers are composite.