{"id":1666,"date":"2020-09-06T20:05:11","date_gmt":"2020-09-06T18:05:11","guid":{"rendered":"http:\/\/matma.com.pl\/?p=1666"},"modified":"2020-09-07T21:40:06","modified_gmt":"2020-09-07T19:40:06","slug":"i-rodzaje-liczb-system-rzymski-zaokraglanie-liczb","status":"publish","type":"post","link":"http:\/\/matma.com.pl\/?p=1666","title":{"rendered":"I. Rodzaje liczb. System rzymski. Zaokr\u0105glanie liczb."},"content":{"rendered":"<p><span style=\"color: #339966; font-family: 'book antiqua', palatino, serif;\"><strong>Rodzaje liczb<\/strong><\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">liczby naturalne-s\u0105 to liczby dodatnie ca\u0142kowite plus zero. Zbi\u00f3r liczb naturalnych mo\u017cemy zapisa\u0107 w postaci <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;0,1,2,3,...&amp;space;\\right&amp;space;\\}\" alt=\"\\left \\{ 0,1,2,3,... \\right \\}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">liczby ca\u0142kowite- s\u0105 to wszystkie liczby naturalne i ich liczby do nich przeciwne. Zbi\u00f3r liczb ca\u0142kowitych mo\u017cemy zapisa\u0107 w postaci <img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\left&amp;space;\\{&amp;space;...,-2,-1,0,1,2,...&amp;space;\\right&amp;space;\\}\" alt=\"\\left \\{ ...,-2,-1,0,1,2,... \\right \\}\" align=\"absmiddle\" \/><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">liczby wymierne- s\u0105 to liczby, kt\u00f3re da si\u0119 zapisa\u0107 w postaci u\u0142amka zwyk\u0142ego<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">liczby niewymierne- s\u0105 to liczby, kt\u00f3rych nie da si\u0119 zapisa\u0107 w postaci u\u0142amka zwyk\u0142ego<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #339966; font-family: 'book antiqua', palatino, serif;\"><strong>Liczby w systemie rzymskim<\/strong><\/span><\/p>\n<table style=\"width: 62.4892%; height: 46px;\">\n<tbody>\n<tr style=\"height: 23px;\">\n<td style=\"width: 9.53182%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>I<\/strong><\/em><\/span><\/td>\n<td style=\"width: 8.90052%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>V<\/strong><\/em><\/span><\/td>\n<td style=\"width: 9.18974%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>X<\/strong><\/em><\/span><\/td>\n<td style=\"width: 9.47258%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>L<\/strong><\/em><\/span><\/td>\n<td style=\"width: 9.73223%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>C<\/strong><\/em><\/span><\/td>\n<td style=\"width: 9.77702%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>D<\/strong><\/em><\/span><\/td>\n<td style=\"width: 8.70141%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\"><em><strong>M<\/strong><\/em><\/span><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"width: 9.53182%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">1<\/span><\/td>\n<td style=\"width: 8.90052%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">5<\/span><\/td>\n<td style=\"width: 9.18974%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">10<\/span><\/td>\n<td style=\"width: 9.47258%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">50<\/span><\/td>\n<td style=\"width: 9.73223%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">100<\/span><\/td>\n<td style=\"width: 9.77702%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">500<\/span><\/td>\n<td style=\"width: 8.70141%; text-align: center; height: 23px; border-style: solid;\"><span style=\"font-family: 'book antiqua', palatino, serif;\">1000<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Aby poprawnie pos\u0142ugiwa\u0107 si\u0119 tymi liczbami musimy stosowa\u0107 si\u0119 do kilku\u00a0zasad:<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Obok siebie mo\u017cemy umie\u015bci\u0107 trzy jednakowe znaki spo\u015br\u00f3d: <em>I, X, C, M<\/em><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Obok siebie nie mo\u017cemy umie\u015bci\u0107 dw\u00f3ch takich samych znak\u00f3w spo\u015br\u00f3d: <em>V, L, D<\/em><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Gdy po znaku wi\u0119kszym wyst\u0119puje znak mniejszy, w\u00f3wczas dodajemy do siebie warto\u015bci tych znak\u00f3w np. <em>XV=10+5=15<\/em><\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Gdy przed znakiem wi\u0119kszym wyst\u0119puje znak mniejszy, w\u00f3wczas od warto\u015bci wi\u0119kszej odejmujemy mniejsz\u0105, przy czym taka kolejno\u015b\u0107 mo\u017ce wyst\u0119powa\u0107 tylko sze\u015b\u0107 razy, mianowicie:<\/span>\n<ul>\n<li><em><span style=\"font-family: 'book antiqua', palatino, serif;\">IV-5-1=4<\/span><\/em><\/li>\n<li><em><span style=\"font-family: 'book antiqua', palatino, serif;\">IX=10-1=9<\/span><\/em><\/li>\n<li><em><span style=\"font-family: 'book antiqua', palatino, serif;\">XL=50-10=40<\/span><\/em><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\"><em>XC=100-10=90<\/em><\/span><\/li>\n<li><em><span style=\"font-family: 'book antiqua', palatino, serif;\">CD=500-100=400<\/span><\/em><\/li>\n<li><em><span style=\"font-family: 'book antiqua', palatino, serif;\">CM=1000-100=900<\/span><\/em><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><span style=\"color: #339966; font-family: 'book antiqua', palatino, serif;\"><span style=\"color: #333333;\"><span style=\"color: #339966;\"><strong>System dziesi\u0105tkowy<\/strong><\/span><br \/>\nPami\u0119ta\u0107 nale\u017cy, w kt\u00f3rym miejscu znajduje si\u0119 konkretna cyfra w danej liczbie, czyli jak\u0105 pozycje zajmuje.<\/span><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img fetchpriority=\"high\" decoding=\"async\" class=\" wp-image-198 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/pozycje-liczb-300x194.png\" sizes=\"(max-width: 464px) 100vw, 464px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/pozycje-liczb-300x194.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/pozycje-liczb.png 582w\" alt=\"\" width=\"464\" height=\"300\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Nast\u0119pnie, \u017ceby by\u0142o \u0142atwiej przeczyta\u0107 du\u017c\u0105 liczb\u0119 grupujemy j\u0105 po trzy cyfry zaczynaj\u0105c od ko\u0144ca. W naszym przypadku liczba b\u0119dzie wygl\u0105da\u0107 nast\u0119puj\u0105co<img decoding=\"async\" class=\"alignnone wp-image-203 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/grupy-w-liczbie-300x90.png\" sizes=\"(max-width: 250px) 100vw, 250px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/grupy-w-liczbie-300x90.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/07\/grupy-w-liczbie.png 432w\" alt=\"\" width=\"250\" height=\"75\" \/>tak zapisana cyfr\u0119 \u0142atwo przeczyta\u0107- jeden milion dwie\u015bcie trzydzie\u015bci cztery tysi\u0105ce pi\u0119\u0107set sze\u015b\u0107dziesi\u0105t siedem.<\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif; color: #339966;\"><strong>Zaokr\u0105glanie liczb<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zaokr\u0105glanie liczby jest jednym z najprostszych temat\u00f3w na matematyce. Zapisuj\u0105c tak\u0105 liczb\u0119, zamiast znaku \u201c=\u201d pos\u0142ugujemy si\u0119 symbolem\u201d\u00a0<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\approx\" alt=\"\\approx\" align=\"absmiddle\" \/>\u201c, kt\u00f3ry czytamy: r\u00f3wny w przybli\u017ceniu. Aby zaokr\u0105gli\u0107 dan\u0105 liczb\u0119, najpierw musimy wybra\u0107 do, kt\u00f3rego miejsca zaokr\u0105glamy nasz\u0105 liczb\u0119 (pozycja cyfry w liczbie).<\/span><\/p>\n<ul>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Zaokr\u0105glanie do rz\u0119du dziesi\u0105tek \u2013 patrzymy na cyfr\u0119 jedno\u015bci i je\u015bli, cyfra ta jest mniejsza od 5 to cyfr\u0119 dziesi\u0105tek zostawiamy bez zmian, a cyfr\u0105 jedno\u015bci staje si\u0119 0 (zaokr\u0105glamy w d\u00f3\u0142 &#8211; z niedomiarem) . Je\u015bli, cyfra w rz\u0119dzie jedno\u015bci jest wi\u0119ksza lub r\u00f3wna 5 to cyfr\u0119 dziesi\u0105tek zwi\u0119kszamy o jeden, a w miejscu jedno\u015bci stawiamy 0 (zaokr\u0105glenie w g\u00f3r\u0119 &#8211; z nadmiarem).<\/span><\/li>\n<\/ul>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><img decoding=\"async\" class=\"wp-image-1062 aligncenter\" src=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/zaokr%C4%85glanie-10-300x197.png\" sizes=\"(max-width: 223px) 100vw, 223px\" srcset=\"http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/zaokr\u0105glanie-10-300x197.png 300w, http:\/\/matma.com.pl\/wp-content\/uploads\/2020\/08\/zaokr\u0105glanie-10.png 380w\" alt=\"\" width=\"223\" height=\"147\" \/><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Analogicznie zaokr\u0105glamy liczby do setek, tysi\u0119cy, setek tysi\u0119cy i tak dalej.<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ad 1<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Zapisz w systemie dziesi\u0105tkowym liczby<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">MCDLXXIX=1000+400+50+10+10+9=1479<\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong>Zadanie 1<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zapisz w systemie dziesi\u0105tkowym liczby<\/span><\/p>\n<ol>\n<li style=\"list-style-type: none;\">\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">MCDLXX<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">DCIV<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">MCCXXXIV<\/span><\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ad 2\u00a0<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Zapisz w systemie rzymskim liczb\u0119<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">3296=MMMCCXCVI<\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong>Zadanie 2<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zapisz w systemie rzymskim liczb\u0119<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">1999<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">574<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">najwi\u0119ksz\u0105 jak\u0105 si\u0119 da stosuj\u0105c zasady dotycz\u0105ce zapisywania liczb w systemie rzymskim<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ad 3<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Ile lat min\u0119\u0142o od roku CCLVII do roku CMXLVII\u00a0<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">\u00a0CCXLVII=247<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">CMXLVII=947<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">947-247=700<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Odpowied\u017a: Min\u0119\u0142o 700 lat.<\/span><\/p>\n<ol>\n<li style=\"list-style-type: none;\"><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong>Zadanie 3<\/strong><\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Ile lat min\u0119\u0142o od 1 r. p. n. e. do 2 r. n.e.?<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">Ile lat min\u0119\u0142o od roku CMXLII do roku MMXIX?<\/span><\/li>\n<\/ol>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Przyk\u0142ad 4<\/span><\/p>\n<p><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">Zaokr\u0105glij podan\u0105 liczb\u0119 z dok\u0142adno\u015bci\u0105 do tysi\u0119cy<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">75 412\u224875000<\/span><\/li>\n<li><span style=\"color: #808080; font-family: 'book antiqua', palatino, serif;\">1 234 567\u22481 235 000<\/span><\/li>\n<\/ol>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\"><strong>Zadanie 4<\/strong><\/span><\/p>\n<p><span style=\"font-family: 'book antiqua', palatino, serif;\">Zaokr\u0105glij liczb\u0119 918273 z dok\u0142adno\u015bci\u0105\u00a0<\/span><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">do tysi\u0119cy<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">do dziesi\u0105tek tysi\u0119cy<\/span><\/li>\n<li><span style=\"font-family: 'book antiqua', palatino, serif;\">do setek<\/span><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>Rodzaje liczb liczby naturalne-s\u0105 to liczby dodatnie ca\u0142kowite plus zero. Zbi\u00f3r liczb naturalnych mo\u017cemy zapisa\u0107 w postaci liczby ca\u0142kowite- s\u0105 to wszystkie liczby naturalne i ich liczby do nich przeciwne. Zbi\u00f3r liczb ca\u0142kowitych mo\u017cemy zapisa\u0107 w postaci liczby wymierne- s\u0105 to liczby, kt\u00f3re da si\u0119 zapisa\u0107 w postaci u\u0142amka zwyk\u0142ego liczby niewymierne- s\u0105 to liczby, [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[45],"tags":[],"class_list":["post-1666","post","type-post","status-publish","format-standard","hentry","category-egzamin-osmoklasisty"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.1 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>I. Rodzaje liczb. System rzymski. 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Zbi\u00f3r liczb ca\u0142kowitych mo\u017cemy zapisa\u0107 w postaci liczby wymierne- s\u0105 to liczby, kt\u00f3re da si\u0119 zapisa\u0107 w postaci u\u0142amka zwyk\u0142ego liczby niewymierne- s\u0105 to liczby, [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"http:\/\/matma.com.pl\/?p=1666\" \/>\n<meta property=\"og:site_name\" content=\"Matma.com.pl\" \/>\n<meta property=\"article:published_time\" content=\"2020-09-06T18:05:11+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2020-09-07T19:40:06+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/latex.codecogs.com\/gif.latex?left&amp;space;&amp;space;0,1,2,3,...&amp;space;right&amp;space;\" \/>\n<meta name=\"author\" content=\"lucynabartczak99\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"lucynabartczak99\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"http:\/\/matma.com.pl\/?p=1666#article\",\"isPartOf\":{\"@id\":\"http:\/\/matma.com.pl\/?p=1666\"},\"author\":{\"name\":\"lucynabartczak99\",\"@id\":\"https:\/\/matma.com.pl\/#\/schema\/person\/b54229c3e035dea49ef8c166c5c63f1e\"},\"headline\":\"I. 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