Number and Place Value

In Key Stage 2 you work with much bigger numbers than before — all the way up to ten million (10,000,000). You also meet negative numbers and Roman numerals. In this lesson you will learn to read, write, order, compare, and round large numbers with confidence.

Place Value: Understanding Large Numbers

Every digit in a number has a place value — its position tells you exactly how much it is worth.

Here are the seven place value columns:

Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
M	HTh	TTh	Th	H	T	O

Example: 3,456,789

M	HTh	TTh	Th	H	T	O
3	4	5	6	7	8	9

3 is worth 3,000,000 (three million)
4 is worth 400,000 (four hundred thousand)
5 is worth 50,000 (fifty thousand)
6 is worth 6,000 (six thousand)
7 is worth 700 (seven hundred)
8 is worth 80 (eighty)
9 is worth 9 (nine)

So 3,456,789 = 3,000,000 + 400,000 + 50,000 + 6,000 + 700 + 80 + 9.

Commas are written every three digits from the right to make large numbers easier to read.

Ordering and Comparing Numbers

To compare two numbers, look at the highest place value first. Move right until you find a difference.

Example: Compare 4,283,100 and 4,289,000

Millions: both 4 — same.
Hundred thousands: both 2 — same.
Ten thousands: both 8 — same.
Thousands: 3 vs 9 — 9 is larger.
So 4,289,000 > 4,283,100.

Example: Order from smallest to largest: 23,450 | 23,045 | 24,350 | 23,540

First, 24,350 has the most ten-thousands, so it is the largest.
The other three all start 23,___. Look at thousands: 0 < 4 < 5.
Order: 23,045 < 23,450 < 23,540 < 24,350.

Rounding Numbers

Rounding replaces a number with a nearby round number that is easier to use — for example when estimating.

The rule: Look at the digit immediately to the right of the place you are rounding to.

If it is 5 or more — round up.
If it is 4 or less — round down (the digit stays the same).

Rounding to the nearest 10:

43 rounds to 40 (ones digit is 3)
47 rounds to 50 (ones digit is 7)
85 rounds to 90 (ones digit is 5 — round up)

Rounding to the nearest 1,000:

4,430 rounds to 4,000 (hundreds digit is 4)
4,700 rounds to 5,000 (hundreds digit is 7)
4,500 rounds to 5,000 (hundreds digit is 5 — round up)

Rounding to the nearest 1,000,000:

3,470,000 rounds to 3,000,000
3,720,000 rounds to 4,000,000

Negative Numbers

Negative numbers are less than zero. They sit to the left of zero on a number line.

... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...

Key rule: The further left from zero, the smaller the number.

-10 is less than -3, because -10 is further left.

Real-life uses: temperature below zero, depths below sea level, bank overdrafts.

Calculating with negative numbers:

A temperature of -4 degrees rises by 7. New temperature: -4 + 7 = 3
What is the difference between -3 and 5? Count from -3 up to 5: that is 8 steps. Difference = 8.
A temperature of 2 degrees falls by 6. New temperature: 2 - 6 = -4

Counting in Multiples

Counting in multiples means skip-counting — jumping by the same number each time.

Year 3 multiples you must know:

Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 ...
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80 ...
Multiples of 50: 50, 100, 150, 200, 250, 300 ...
Multiples of 100: 100, 200, 300, 400, 500 ...

Year 4 multiples you must also know:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60 ...
Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, 70 ...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 ...
Multiples of 25: 25, 50, 75, 100, 125, 150 ...
Multiples of 1,000: 1,000, 2,000, 3,000, 4,000 ...

Using multiples to count in steps:

Count on in 8s from 24: 24, 32, 40, 48, 56 ...
Count back in 6s from 42: 42, 36, 30, 24, 18 ...
Count on in 25s from 75: 75, 100, 125, 150 ...

Tip: A multiple of 4 is always even. A multiple of 9 has digits that add up to 9 (or a multiple of 9) — for example, 63: 6 + 3 = 9.

Roman Numerals

Roman numerals use letters to represent numbers. You need to know these up to 1,000.

Roman	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1,000

The subtraction rule: when a smaller numeral appears directly before a larger one, subtract it.

IV = 4, IX = 9, XL = 40, XC = 90, CD = 400, CM = 900

The addition rule: when a smaller numeral appears after a larger one, add it.

VI = 6, XI = 11, LX = 60, DI = 501

Examples:

XLVII = 40 + 7 = 47
MCMXCIX = 1000 + 900 + 90 + 9 = 1999
MMXXIV = 2000 + 20 + 4 = 2024

Practice

What is the value of the digit 6 in 4,621,300? 600,000
Round 3,470,000 to the nearest million. 3,000,000
Round 82,549 to the nearest thousand. 83,000
Order smallest to largest: 1,054,000 | 1,005,400 | 1,045,000. 1,005,400 < 1,045,000 < 1,054,000
A temperature is -6 degrees. It drops by 4 degrees. New temperature? -10 degrees
What is the Roman numeral for 44? XLIV
What number does MMCDLVI represent? 2,456
What is 10,000 more than 349,500? 359,500