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Numbers (I)

9 min read

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.
Place valueA place value chart for the number 345.67: 3 hundreds, 4 tens, 5 ones, then after the decimal point 6 tenths and 7 hundredths.Hundreds3Tens4Ones5.Tenths6Hundredths7345.67 = 300 + 40 + 5 + 0.6 + 0.07

Kinds of numbers

Number sets you meet first
NameNumbersExample
Natural (counting) numbers1, 2, 3, 4, …Count 7 goats
Whole numbers0, 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.
Adding and subtracting on a number lineA number line from minus five to five. Adding a positive number moves right and subtracting moves left. The example 2 plus minus 5 shows a hop of 5 to the left from 2, landing on minus 3.-5-4-3-2-10123452 − 5 = −3negative numberspositive numbers
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?

  1. Rising means adding.
  2. 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.
Fractions