Chapter 1The Decimal Number System

The System

• Decimal refers to 10 10 symbols specifically 0 – 9 Example

•In the number 5,264 What weight does the 2 have What weight does the 4 have What weight does the 5 have What weight does the 6 have

The System

Bill R. Deem and Tony ZanniniElectronics and Computer Math, Eighth Edition

Copyright ©2006 by Pearson Education, Inc.

Upper Saddle River, New Jersey 07458All rights reserved.

Decimal Fractions

• A fraction with either Ten or a multiple of ten as the denominator

10, 100, 1000, etc

• Examples 9 thousands = 9/1000 0.00039 = 3.9/10000 = 39/100,000 = 390/1M

57.045 = 57 45/1000 27 7/100 = 27.07

Rounding Off Numbers

• Common in problem solving Simplifies calculation of approximate answer

Used to eliminate precision that exceeds resolution of accuracy

• Examples Round 72, 348 to nearest tens = 72,350

Round 47.062 to nearest tenth and ten•Yields: 47.1 and 50

Operations on Signed Numbers

• Addition & Subtraction Signed numbers per Number Line

6-3 = 3 OR 6 + (-3) = 3

• Multiplication and Division Few and simple rules for sign numbers

Operations on Signed Numbers

• Multiplication and Division Rules for Signed Numbers

1. ( + ) * ( + ) = ( + )2. ( + ) * ( - ) = ( - )3. ( - ) * ( + ) = ( - )4. ( - ) * ( - ) = ( + )

Change denominators to reciprocals and the same rules apply to division

Order of operations• Definitions

Mathematical Term - Quantity preceded by a ‘+’ or ‘-’ sign

Mathematical Expression – quantity with one or more terms

• Order of Operations Without ( ) or other grouping signs

•Do multiplications/divisions first for all terms

•Then add/subtract the terms

Order of operations• Order of Operations

With ( ) or other grouping signs•In the inner most grouping

Do multiplications/divisions first for all terms

Then add/subtract the terms

•Remove inner most grouping marks Do multiplications/divisions first for all terms

Then add/subtract the terms

•Repeat above step until resolved