Base Ten Numeration · Mathematics

Place value: where a digit sits matters

We write numbers with ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. This is the base ten system. A digit's value depends on its place. In 4 305 the 4 is in the thousands place, so it means 4 000.

Each place is ten times bigger than the place to its right.

Kinds of numbers

Number sets you meet first
Name	Numbers	Example
Natural (counting) numbers	1, 2, 3, 4, …	Count 7 goats
Whole numbers	0, 1, 2, 3, …	0 goats in the pen
Integers	…, −3, −2, −1, 0, 1, 2, 3, …	Temperature −2 °C

Integer: Any whole number, positive, negative or zero. Negative integers lie to the left of zero on the number line.

Adding and subtracting integers

Adding a positive moves right. Adding a negative (or subtracting a positive) moves left.

Try itAdd integers on the number line

Move and and watch the sum.

Worked exampleIntegers in a story

At dawn the temperature is . By noon it rises by . What is it at noon?

Rising means adding.
From −3 move 9 steps to the right. Three steps reach 0, six more reach 6.

Answer: The temperature at noon is 6 °C.

Check yourself What is the value of the digit 7 in 27 481?

Check yourself Which is the smallest integer?

Key terms

Place value: The value a digit has because of its position.
Integer: A positive or negative whole number, or zero.
Number line: A line where numbers are placed in order, smaller on the left.

Summary

Base ten uses ten digits; each place is ten times the one on its right.
Natural numbers start at 1, whole numbers at 0, integers include negatives.
On the number line, adding moves right and subtracting moves left.