Muravanegumi

Muchidzidzo masvomhu, muravanegumi (decimal system in English) zvinoreva tsika inotevedzwa yokuverenga nokunyora nhamba kuchishandiswa gumi sehwaro hwekuverenga nhamba. Patsika iyi panoshandiswa mavara gumi anoti: 0,1,2,3,4,5,6,7,8,9 kuratidza huwandu chero hupi hunoverengeka. Apa nhamba dzinenge dzakarongwa nenzira yokuti dzinokwanisa kufananidzwa negumi kana kuti nezvitsama zvegumi. Pamaverengero anoitwa nhamba paChiShona tinoona nhamba dzakarongwa sezvizvi:

• Pamawoko edu maviri tinokwanisa kuverenga kusvika pana gumi. Zvichienda mberi tinenge towumba nhamba zvichibva pana gumi. Nhamba inotevera gumi (10) inodanwa kunzi gumi nerimwe (11), kwouya gumi nembiri (12), gumi nenhatu (13), gumi nemana (14), zvichingodaro.

• Zvimwechetezvo tikaverenga minwe yemawoko kaviri tinosvika pana makumi maviri (20). Zvadaro kunenge kwotevera, makumi maviri nerimwe (21), makumi maviri nembiri (22), makumi maviri nenhatu, zvichingoenda zvakadaro.

• Tikaramba tichienda tinosvika pamakumi gumi anodanwa kunzi zana.

• Tsama remakumi zana rinonzi chiuru, zvichingodaro.

Saka pano taona kuti gumi ndihwo hwaro hunoshandiswa pakuwumba tsika yatinoshandisa kuverenga nokunyora nhamba. Tsika iyi yokuverenga negumi inoshandiswa munyika dzose Pasirose asi haiziri iyo yoga tsika inoshandiswa kuverenga nhamba. Kare-kare vagari veBabylon vaishandisa makumi matanhatu sehwaro pakuverenga nhamba. Pari nhasi macomputer anoshandisa tsika yemuravanembiri (binary system) inova inotora nhamba dzinoti 0 na 1 dzoga.

Kupiwa kwezita

Shoko reEnglish rokuti decimal rinoreva kuti Pertaining to tens or proceeding in tens. Apa ndipo paturikirwa kuti kuChiShona kunzi kuravanegumi nokuti marongerwo enhamba kana dzichiverengwa dzinotevedza gumi nezvitsama zvegumi.

Nokumwe kutaura tsika inoshandiswa pamuravanegumi ingadzi rugumidzira, kana toshandura kuEnglish zvoreva kuti – ‘’following tens or by way of ten’’.

Manyorerwo eNhamba

Pamuravanegumi nhamba dzinonyorwa kuchishandiswa mavara gumi akasiyana anoti: 0, 1,2,3,4,5,6,7,8,9. Panotangwa kuverengwa nhamba mavara aya anodanwa akatevedzana saizvozvi. Mushure ma 9 hakuchina rimwe vara rakasiyana. Panhamba inotevera panowedzerwa chimwe chinzvimbo mavara otanga kuchidzokorora. Saka panhamba inotevera 9 panonyorwa pachitsvetwa 1 achiteverwa na 0 kuti pave nenhamba inonzi 10.

Tsika yokuronga nhamba muzvinzvimbo zvakasiyana tichaidana kuti tsika yezvinzvimbo zvenhamba - positional numeral system. Tsika iyi inopa vara huhombe hwakasiyana zvichienderana nokuti vara ratsvetwa pachinzvimbo chipi. Kana vara 1 riri panzvimbo yokutanga anomirira huwandu hwechinhu chimwe. Kana vara 1 riri pachinzvimbo chechipiri anomirira huwandu hwezvinhu gumi, apa nzvimbo yokutanga inenge yakanyorwa vara 0. Panokwidzwa nhamba kamwe nzvimbo yokutanga kuruboshwe inoshandurwa kuenda pana 1 kuti nhamba ichiva 11; izvi zvoreva kuti pava negumi nerimwe.

Huhombe wenzvimbo paMuravanegumi

Zvinzvimbo zviri paMuravanegumi zvinomirira huhombe hwakasiyana; hazvinei kuti vara riri pazvinzvimbo izvi ringange riri rakafanana. Huhombe uhwu hunotaridzwa nemuradanuro wa 10 nepawa rinokura zvichienda kuruboshwe. Somuenzaniso kana nhamba 3523 ichipenengurwa inonyorwa sezvizvi:

$3523=3\times 10^{3}+5\times 10^{2}+2\times 10^{1}+3\times 10^{0}$.

Izvi zvinoreva kuti 3 ari panzvimbo yekutanga kurudyi anomirira huwandu hwechinhu chimwe. Mumwe 3 ari pachinzvimbo chechina kubva kurudyi anomirira huwandu hwezviuru zvitatu.

Nzvimbo dzenhamba idzi dzinopiwa mazita adzo sezvizvi:

• 10⁰ inonzi Zvibodzi, Units or Ones kuEnglish.

• 10¹ inonzi Makumi, Tens ku English.

• 10² inonzi Mazana, Hundreds ku English.

• 10³ inonzi Zviuru, Thousands ku English.

• 10⁴ inonzi Makumi reZviuru, Ten Thousands ku English.

• 10⁵ inonzi Zana reZviuru, Hundred Thousands ku English.

• 10⁶ inonzi Miliyoni, Million ku English.

• 10⁷ inonzi Makumi eMiliyoni, Tens of Millions ku English.

• 10⁸ inonzi Mazana eMiliyoni, Million ku English.

Zvakafanira kuti tinoensane kuti marongerwo akaitwa mapawa agumi pamusoro, kana onyorwa senhamba anenge akarongeka achibva kurudyi kuenda kuruboshwe. Shoko rokuti zvibodzi rashaniswa kuturikira units rinobva kuchiKorekore; chibodzi rinoreva chimwe (1), pakuwanda konzi zvibodzi.

Tichitarisa chero ipi tsika inoshandisa hwaro -b, tinoona ine mavara ane huwandu b, uye nhamba

$a_{3}a_{2}a_{1}a_{0}=a_{3}\times b^{3}+a_{2}\times b^{2}+a_{1}\times b^{1}+a_{0}\times b^{0}$

(Zvakakosha tionesane kuti $a_{3}a_{2}a_{1}a_{0}$ anomirira kutevedzana pamarongerwo emavara, kwete rutsamo)

Chimedu paMuravanegumi

Shoko rokuti chimedu cheMuravanegumi (decimal fraction) rinoreva chimedu chine chisazita chinonyorwa ari gumi ari kuradanurwa nepawa rakakodzera. Chimedu cheMuravanegumi chinopangidzwa kuchinyorwa koma kuruboshwe kwemberengi; kana zvadai chisaazita rinenge risisanyorwe. Ana zero vanotsvetwa pakati pekoma nemberengi kana zvakakodzera kuti nhamba dzemberengi (numerator) dzigonyorwa panzvimbo yakakodzera.

Ngatitarisei somuenzaniso zvidimbu zvinotevera: 8/10, 83/100, 83/1000, and 8/10000; kana zvoshandurwa kupinda paMuravanegumi zvinonyorwa sezvizvi: 0.8, 0.83, 0.083, and 0.0008.

Mazita eZvimedu paMuravanegumi

Nhamba dziri kurudyi kwapoyindi paMuravanegumi dzinopihwawo mazita sezvizvi:

• 10^-1 kana 1/10 inonzi Chimwe paGumi, Tenths kuEnglish.

• 10^-2 kana 1/100 inonzi Chimwe paZana, Hundredths ku English.

• 10^-3 kana 1/1,000 inonzi Chimwe paChiuru, Thousandths ku English.

• 10^-4 kana 1/10,000 inonzi Chimwe paZviuru Gumi, Ten Thousandths ku English.

• 10^-5 kana 1/100,000 inonzi Chimwe paZviuru Zana, Hundred Thousandths ku English.

• 10^-6 kana 1/1,000,000 inonzi Chimwe paMiriyoni, Millionth ku English.

Tsika

• Chegumi ndicho chikamu chegoho kana hupfumi chakarayirwa kuti vana vaIsrayeri vapote vachipa kuna Mwari