Rounding for beginners- MA100 Cheat Sheet PDF

Preview

Summary

Rounding for beginners- MA100 Cheat Sheet practice...

Description

Mathematics Assistance Centre A unit within the Centre for Student Success www.wlu.ca/mac

Reference Sheet:

Round-to-even Rounding:

Rounding Rounding is the process of eliminating non-significant digits, for a required degree of accuracy. There are several methods to rounding numbers; this reference covers two common ones. Most methods differ in the way to round when the first non-significant digit is 5.

Round-to-even rounding, also known as unbiased rounding or convergent rounding, is the method commonly seen when working with statistics. To round numbers using this method, follow these steps: 1. Determine the required accuracy (ie. the rounding digit) 2. Look at the digit to the right of the rounding digit. • If this digit is 6 or greater, add 1 to the rounding digit. • If this digit is 4 or less, retain the original rounding digit.

Symmetric Arithmetic Rounding: Symmetric arithmetic rounding is the most commonly used method in math, and is the method you’ve probably seen before. To round numbers using this method, follow these steps: 1. Determine the required accuracy (ie. the rounding digit)

• If this digit is 5 followed by one or more nonzero digits, add 1 to the rounding digit. • If this digit is 5 and followed by only zeros, adjust the rounding digit to the nearest even digit (ie. add 1 to the rounding digit if it is currently odd, or retain the rounding digit if it is currently even).

2. Look at the digit to the right of the rounding digit. • If this digit is 5 or greater, add 1 to the rounding digit, and drop/change all the digits to the right of it to 0 (round up). • If this digit is less than 5, retain the original rounding digit and drop/change all the digits to the right of it to 0 (round down).

rounded to rounded to rounded to rounded to

34.0667 2.164503 101.245 12350

rounded rounded rounded rounded

to to to to

the the the the

hundredths thousandths hundredths thousands

→ → → →

34.07 2.165 101.24 12400

Rounding in Calculations:

Examples: 4.1816 5.67 2367 15734

Examples:

the the the the

hundredths tenths tens thousands

→ → → →

4.18 5.7 2370 16000

Note: Whole numbers to the right of the rounding digit get changed to a 0, while decimal numbers to the right are dropped. Due to the rules of symmetric arithmetic rounding, sometimes when working with large samples in statistics, symmetric arithmetic rounding can lead to slightly higher results from calculations. Thus, roundto-even rounding is used to ensure a large set of data is not altered by rounding.

Rounding can often result in inaccurate answers when doing multi-stepped calculations, specifically when rounded numbers are involved in arithmetic operations with other rounded numbers. There are two main methods to round when doing calculations, to minimize the possibility of rounding errors: 1. Retain an extra non-significant digit for intermediate answers. 2. If using a calculator, for each arithmetic operation, retain all the digits using the memory/storage feature of your calculator. Once you reach your final answer, implement the rules of rounding....