Skip to content Skip to navigation Skip to collection information

OpenStax_CNX

You are here: Home » Content » Siyavula textbooks: Wiskunde (Graad 11) » Foutgrense

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • FETWisk display tagshide tags

    This module and collection are included inLens: Siyavula: Wiskunde (Gr 10 - 12)
    By: Siyavula

    Module Review Status: Approved
    Collection Review Status: Approved

    Click the "FETWisk" link to see all content affiliated with them.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.
 

Foutgrense - Graad 11

Ons het gesien dat getalle rasionaal of irrasionaal kan wees en ons het gesien hoe om getalle af te rond. In 'n berekening wat meer as een stap het, is dit beter om die afronding in die heel laaste stap te doen.

By voorbeeld, as jy gevra word om 33+1233+12 te skryf as 'n desimale getal afgerond tot twee desimale plekke, is daar twee maniere om dit te doen.

Metode 1

3 3 + 12 = 3 3 + 4 · 3 = 3 3 + 2 3 = 5 3 = 5 × 1 , 732050808 ... = 8 , 660254038 ... = 8 , 66 3 3 + 12 = 3 3 + 4 · 3 = 3 3 + 2 3 = 5 3 = 5 × 1 , 732050808 ... = 8 , 660254038 ... = 8 , 66
(1)

Metode 2

3 3 + 12 = 3 × 1 , 73 + 3 , 46 = 5 , 19 + 3 , 46 = 8 , 65 3 3 + 12 = 3 × 1 , 73 + 3 , 46 = 5 , 19 + 3 , 46 = 8 , 65
(2)

In hierdie voorbeeld sien ons dat Metode 1 die antwoord gee as 8,66 terwyl Metode 2 die antwoord gee as 8,65. Die antwoord van Metode 1 is meer akkuraat want die uitdrukking is so ver as moontlik vereenvoudig voordat die antwoord afgerond is.

In die algemeen is dit beter om 'n uitdrukking sover as moontlik te vereenvoduig voordat jy jou sakrekenaar gebruik om die antwoord in desimale vorm te gee.

leidraad:

Vereenvoudiging en Akkuraatheid

Dit is nodig om alle uitdrukkings sover as moontlik te vereenvoudig voordat antwoorde afgerond word. Dit het 'n invloed op die akkuraatheid van jou antwoord.

Exercise 1: Vereenvoudiging en Akkuraatheid

Bereken 543+163543+163. Gee die antwoord korrek tot drie desimale plekke.

Solution

  1. Stap 1. Vereenvoudig die uitdrukking :
    54 3 + 16 3 = 27 · 2 3 + 8 · 2 3 = 27 3 · 2 3 + 8 3 · 2 3 = 3 2 3 + 2 2 3 = 5 2 3 54 3 + 16 3 = 27 · 2 3 + 8 · 2 3 = 27 3 · 2 3 + 8 3 · 2 3 = 3 2 3 + 2 2 3 = 5 2 3
    (3)
  2. Stap 2. Herskryf enige irrasionale getalle as desimale getalle :
    5 2 3 = 5 × 1 , 25992105 ... = 6 , 299605249 ... = 6 , 300 5 2 3 = 5 × 1 , 25992105 ... = 6 , 299605249 ... = 6 , 300
    (4)
  3. Stap 3. Skryf die finale antwoord tot die gevraagde aantal desimale plekke. :
    6 , 299605249 ... = 6 , 300 tot drie desimal plekke 6 , 299605249 ... = 6 , 300 tot drie desimal plekke
    (5)

    543+163=6,300543+163=6,300 tot drie desimale plekke.

Exercise 2: Vereenvoudiging en Akkuraatheid 2

Bereken x+1+13(2x+2)-(x+1)x+1+13(2x+2)-(x+1) as x=3,6x=3,6. Gee die antwoord korrek tot twee desimale plekke.

Solution

  1. Stap 1. Vereenvoudig die uitdrukking :
    x + 1 + 1 3 ( 2 x + 2 ) - ( x + 1 ) = x + 1 + 1 3 2 x + 2 - x - 1 = x + 1 + 1 3 x + 1 = 4 3 x + 1 x + 1 + 1 3 ( 2 x + 2 ) - ( x + 1 ) = x + 1 + 1 3 2 x + 2 - x - 1 = x + 1 + 1 3 x + 1 = 4 3 x + 1
    (6)
  2. Stap 2. Vervang die waarde van xx in die vereenvoudigde uitdrukking :
    4 3 x + 1 = 4 3 3 , 6 + 1 = 4 3 4 , 6 = 2 , 144761059 ... × 4 ÷ 3 = 2 , 859681412 ... 4 3 x + 1 = 4 3 3 , 6 + 1 = 4 3 4 , 6 = 2 , 144761059 ... × 4 ÷ 3 = 2 , 859681412 ...
    (7)
  3. Stap 3. Gee die finale antwoord tot die gevraagde aantal desimale plekke :
    2 , 859681412 ... = 2 , 86 tot twee desimale plekke 2 , 859681412 ... = 2 , 86 tot twee desimale plekke
    (8)

    x+1+13(2x+2)-(x+1)=2,86x+1+13(2x+2)-(x+1)=2,86 (tot twee desimale plekke) as x=3,6x=3,6.

Beduidende syfers

In enige getal is elke syfer wat nie nul is nie, 'n beduidende syfer. Nulle word slegs getel indien hulle tussen twee nie-nul syfers is of aan die einde van die desimale gedeelte van die getal. By voorbeeld, die getal 2000 het 1 beduidende syfer (die 2), maar 2000,02000,0 het 5 beduidende syfers. Skatting van 'n getal word gedoen deur die beduidende syfers uit jou getal (begin by syfer aan regterkant) te verwyder totdat jy die verlangde aantal beduidende syfers het. Rond af soos jy voortgaan. By voorbeeld 6,8276,827 het 4 beduidende syfers, maar as jy dit wil skryf as 'n getal met 3 beduidende syfers, beteken dit dat jy die 7 moet verwyder en oprond, so dit word 6,836,83. Dit is belangrik om te weet wanneer om 'n getal te benader en wanneer nie. Dit is gewoonlik goeie praktyk om slegs getalle te benader wanneer dit absoluut noodsaaklik is, en liewer simbole te gebruik om sekere irrasionale getalle voor te stel (byvoorbeeld ππ). Benadering gebeur eers aan die einde van die berekening. As dit nodig is om 'n getal in die middel van 'n berekening te benader, is dit dikwels goed genoeg om te benader tot 'n aantal desimale plekke.

Collection Navigation

Content actions

Download:

Collection as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Module as:

PDF | EPUB (?)

What is an EPUB file?

EPUB is an electronic book format that can be read on a variety of mobile devices.

Downloading to a reading device

For detailed instructions on how to download this content's EPUB to your specific device, click the "(?)" link.

| More downloads ...

Add:

Collection to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks

Module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need an account to use 'My Favorites'.

| A lens I own (?)

Definition of a lens

Lenses

A lens is a custom view of the content in the repository. You can think of it as a fancy kind of list that will let you see content through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks