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Lesson 3: Decimal Numbers (III).

November 15, 2010

4. Approximating and estimating decimal numbers

 4.1 . Approximating decimal numbers

Rules for rounding decimals:

1. Retain the correct number of decimal places (e.g. 3 for thousandths, 0 for whole numbers).

2. If the next decimal place value is 5 or more, increase the value in the last retained decimal place by 1.

Some uses of rounding are:

  • Checking to see if you have enough money to buy what you want.
  • Getting a rough idea of the correct answer to a problem

Example:

36,74691 rounded to the nearest whole number is 37.

12,34690 rounded to the nearest tenth is 12.3.

89,46917 rounded to the nearest tenth is 89.5.

 50.02139 rounded to the nearest hundredth is 50.02.

Practise rounding on this web.

Practise on this website.

Rule for truncating decimals:

Retain the correct number of decimal places (e.g. 3 for thousandths, 0 for whole numbers).

Example:

Consider the number

5,6341432543653654

To truncate these numbers to 4 decimal digits (to the nearest ten thousandth), we only consider the 4 digits to the right of the decimal point.

The result would be:5,6341  

Note that in some cases, truncating would yield the same result as rounding, but truncation does not round up or round down the digits; it merely cuts off at the specified digit.

4.2. Estimating the sum or the difference of two decimals 

To estimate a sum by rounding:

  • Round each decimal term that will be added or subtracted.
  • Add or subtract the rounded terms.

Now is time to practise. Click on

4.3. Absolute error

 The difference between the exact mathematical value of an operation or number , and the calculated approximation value , considered always positive, (with the absolute value taken) is called the absolute error,

 Δx = |x0  − x|

 In Spanish, we write it:

Ea= |valor exacto  − valor aproximado| 

5. Word problems with decimal numbers

We will finish the lesson with our habituals, Word Problems.

You can practise on the following websites:

Mathgoodies: This is a web when you have solved examples and several exercises.

Kwiznet: Problems with solutions

IXL: Problems you must solve but you can check your solutions and getp explanations.

Here you are a video on solving problems

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