INTRODUCTION TO

DECIMALS

Definitions and Place Value

When we write a number like 45.786 how do we know what it means ? The answer is PLACE VALUE ! Decimal Point (>1 . <1)

45.7864 x 10

5 x 17 x 1/10 8 x 1/100

6 x 1/1000

Powers of 10

Remember that 100, 10, 1, 1/10, 1/100, 1/1000in our decimal places are really powers of 10 !

10 to the power 2 = 10010 to the power 1 = 1010 to the power 0 = 1 10 to the power -1 = 1/1010 to the power -2 = 1/10010 to the power -3 = 1/1000

Place Value and Powers of Ten

What does 2378.4592 mean ? Hint: 2 x 103 + ...

103

102

101

100

10-1

10-2

10-3

10-4

Decimal Point

Quick Exercise

Write the following as a sum of powers of 101) 200

2) 100.5

3) 900.02

4) 30.058

Answers

Write the following as a sum of powers of 101) 204 2 x 102 + 4 x 100 (100 = 1)

2) 100.5 1 x 102 + 5 x 10-1

3) 900.02 9 x 102 + 2 x 10-2

4) 30.058 3 x 101 + 5 x 10-2 + 8 x 10-3

Summary

• Decimal numbers depend on Place Value

• Numbers to the left of the Decimal Point are > 1 (greater than 1) and to the right are < 1 (less than 1 – like fractions !)

• Each column is ten times different to its neighbours