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) 45.786 6 x 1/1000 4 x 10 5 x 1 8 x 1/100 7 x 1/10

Powers of 10 Remember that 100, 10, 1, 1/10, 1/100, 1/1000 in our decimal places are really powers of 10 ! 10 to the power 2 = 100 10 to the power 1 = 10 10 to the power 0 = 1 10 to the power -1 = 1/10 10 to the power -2 = 1/100 10 to the power -3 = 1/1000

Place Value and Powers of Ten What does 2378.4592 mean ? Hint: 2 x 103 + ... 103 101 10-1 10-3 102 100 10-2 10-4 Decimal Point

Quick Exercise Write the following as a sum of powers of 10 200 100.5 900.02 30.058

Answers Write the following as a sum of powers of 10 204 2 x 102 + 4 x 100 (100 = 1) 100.5 1 x 102 + 5 x 10-1 900.02 9 x 102 + 2 x 10-2 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