{"id":1243,"date":"2020-07-11T12:45:02","date_gmt":"2020-07-11T04:45:02","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1243"},"modified":"2020-11-02T23:45:14","modified_gmt":"2020-11-02T15:45:14","slug":"approximation-errors","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/approximation-errors\/","title":{"rendered":"1. \u8fd1\u4f3c\u8207\u8aa4\u5dee (Approximation &#038; Errors)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1243\" class=\"elementor elementor-1243\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-61e248c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"61e248c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-01060f1\" data-id=\"01060f1\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a15c640 elementor-widget elementor-widget-text-editor\" data-id=\"a15c640\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>1.1\u00a0 \u6709\u6548\u6578\u5b57 (Significant Figure)<\/h2><p>\u6240\u8b02\u300c\u6709\u6548\u6578\u5b57\u300d\uff0c\u5176\u5be6\u4fc2\u53d6\u8fd1\u4f3c\u503c\u7684\u4e00\u500b\u65b9\u6cd5\u3002\u65e5\u5e38\u751f\u6d3b\u4e2d\u6211\u5730\u90fd\u7d93\u5e38\u6709\u7528\u5230\u3002<\/p><p>\u4f8b\u5982\u4e00\u500b\u544e\u50f9$15330\u5605205\u5e73\u65b9\u544e\u55ae\u4f4d\uff0c\u5dff\u50f9\u4fc2$3,142,650\u3002\u4f46\u6211\u5730\u4e00\u822c\u90fd\u6703\u8b1b\u500b\u55ae\u4f4d\u503c$3,140,000 \u6216\u503c$3,000,00\u3002 \u7576\u6211\u5730\u8a71\u500b\u55ae\u4f4d\u503c$\u4e09\u767e\u842c\u5605\u6642\u5019\uff0c\u5176\u5be6\u6211\u5730\u53ea\u4fc2\u7747\u4f4f\u7b2c\u4e00\u500b\u6578\u5b57&#8221;3&#8243;\uff0c\u7136\u5f8c\u5c07\u5f8c\u9762\u5605\u6578\u5b57\u505a\u56db\u62fe\u4e94\u5165\u3002\u5176\u5be6\u6211\u5730\u5df2\u7d93\u505a\u5497\u4e00\u6b21\u300c\u6368\u5165\u81f31\u4f4d\u6709\u6548\u6578\u5b57\u300d\u3002<\/p><p>\u4f8b1\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u628a5602\u6368\u5165\u81f32\u4f4d\u6709\u6548\u6578\u5b57\u3002<br \/>\u7b54\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \\(5602 \\approx 5600 \\quad (\u6e96\u78ba\u81f32\u4f4d\u6709\u6548\u6578\u5b57) \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ead1a26 elementor-widget elementor-widget-text-editor\" data-id=\"ead1a26\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>1.2\u00a0 \u8aa4\u5dee<\/h2><p>\u8aa4\u5dee\u4fc2\u6307\u91cf\u5ea6\u51fa\u4f86\u7684\u6578\u503c\u540c\u771f\u5be6\u6578\u503c\u7684\u5dee\u8ddd\u3002<\/p><p>\u9664\u5497\u8aa4\u5dee\u4e00\u8a5e\u4ee5\u5916\uff0c\u4e0b\u9762\u5605\u8a5e\u5f59\u90fd\u7d93\u5e38\u6703\u51fa\u73fe\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\u771f\u5be6\u503c = True Value<br \/>\u771f\u5be6\u5373\u4fc2\u8981\u91cf\u5ea6\u5605\u503c\u5605\u76f4\u5be6\u503c\uff0c\u5514\u597d\u554f\u5230\u5e95\u9ede\u77e5\u3002<\/li><li>\u91cf\u5ea6\u503c = Measured Value<br \/>\u7528\u91cf\u5ea6\u5100\u5668\u5c0d\u4ef6\u7269\u4ef6\u6240\u91cf\u5ea6\u51fa\u569f\u5605\u503c\u3002<\/li><li>\u6e96\u78ba\u5ea6 = Precision<br \/>\u91cf\u5ea6\u5100\u5668\u6bcf\u4e00\u683c\u4e4b\u9593\u8ddd\u3002<br \/>\u4f8b\u5982<ul><li>\u7528\u4e00\u628a\u523b\u67091cm\u30012cm\u30013cm\u5605\u76f4\u5c3a\u53bb\u91cf\u5ea6\u9577\u5ea6\uff0c\u6e96\u78ba\u5ea6\u5c31\u4fc21cm\u3002<\/li><li>\u7528\u4e00\u500b\u6703\u986f\u793a0.5kg\u30011.0kg\u30011.5kg\u30012.0kg\u5605\u96fb\u5b50\u78c5\u53bb\u91cf\u5ea6\u91cd\u91cf\uff0c\u6e96\u78ba\u5ea6\u5c31\u4fc20.5kg\u3002<\/li><\/ul><\/li><li>\u6700\u5927\u8aa4\u5dee = Maximum Error<br \/>\u6307\u91cf\u5ea6\u51fa\u4f86\u7684\u6578\u503c\u540c\u771f\u5be6\u6578\u503c\u7684\u6700\u5927\u5dee\u8ddd\u3002<\/li><li>\u76f8\u5c0d\u8aa4\u5dee = Relative Error<\/li><li>\u767e\u5206\u8aa4\u5dee = Percentage Error<\/li><li>\u4e0a\u9650 = Upper Limit<br \/>\u7576\u77e5\u9053\u500b\u91cf\u5ea6\u503c\u5f8c\uff0c\u771f\u5be6\u503c\u6700\u5927\u7684\u53ef\u80fd\u503c\u3002<br \/>\u4f8b\u5982\u5982\u679c\u5df2\u77e5\u4e00\u672c\u66f8\u5605\u91cd\u91cf\u4fc20.5kg (\u6e96\u78ba\u81f3\u5c0f\u6578\u9ede\u5f8c\u4e00\u500b\u4f4d)\uff0c\u66f8\u5605\u91cd\u91cf\u4e0a\u9650\u4fc20.55kg\u3002\u56e0\u70ba\u5982\u679c\u4fc20.55kg\uff0c\u6309\u300c\u6e96\u78ba\u81f3\u5c0f\u6578\u9ede\u5f8c\u4e00\u500b\u4f4d\u300d\u5605\u539f\u5247\uff0c\u6211\u5730\u8981\u8b1b\u672c\u66f8\u4fc20.6kg\u7684\u3002<\/li><li>\u4e0b\u9650 = Lower Limit<br \/>\u7576\u77e5\u9053\u500b\u91cf\u5ea6\u503c\u5f8c\uff0c\u771f\u5be6\u503c\u6700\u5c0f\u7684\u53ef\u80fd\u503c\u3002<br \/>\u7528\u8fd4\u4e0a\u9762\u5605\u4f8b\u5b50\uff0c\u66f8\u5605\u91cd\u91cf\u4e0b\u9650\u4fc20.45kg\u3002\u56e0\u70ba\u5982\u679c\u4fc20.45kg\u4ee5\u4e0b(\u5373\u59820.445kg)\uff0c\u6309\u300c\u6e96\u78ba\u81f3\u5c0f\u6578\u9ede\u5f8c\u4e00\u500b\u4f4d\u300d\u5605\u539f\u5247\uff0c\u6211\u5730\u8981\u8b1b\u672c\u66f8\u4fc20.4kg\u7684\u3002<\/li><li>\u53ef\u80fd\u7bc4\u570d = Range<br \/>\u4e0b\u9650\u81f3\u4e0a\u9650\u7684\u7bc4\u570d<\/li><\/ul><\/li><\/ul><p>\u7576\u660e\u65e5\u5497\u6bcf\u500b\u8a5e\u5f59\u7684\u610f\u601d\u5f8c\uff0c\u4e0b\u9762\u5605\u516c\u5f0f\u5c31\u61c9\u8a72\u5514\u592a\u96e3\uff1a<\/p><p>\\begin{align}<br \/>\u6700\u5927\u8aa4\u5dee &amp; = \\dfrac{\u6e96\u78ba\u5ea6}{2} \\\\<br \/>\u76f8\u5c0d\u8aa4\u5dee &amp; =\u00a0 \\dfrac{\u6700\u5927\u8aa4\u5dee}{\u91cf\u5ea6\u503c}\u00a0 \u6216\u00a0 \\dfrac{\u6700\u5927\u8aa4\u5dee}{\u76f4\u5be6\u503c} \\quad \\quad\u00a0 (\u901a\u5e38\u4ee5\\dfrac{1}{n}\u8868\u793a\u7b54\u6848) \\\\<br \/>\u767e\u5206\u8aa4\u5dee &amp; =\u3000\u76f8\u5c0d\u8aa4\u5dee \\times 100\\% \\\\<br \/>\u4e0a\u9650 &amp; =\u3000\u91cf\u5ea6\u503c \uff0b \u6700\u5927\u8aa4\u5dee \\\\<br \/>\u4e0b\u9650 &amp; = \u3000\u91cf\u5ea6\u503c \uff0d \u6700\u5927\u8aa4\u5dee \\\\<br \/>\u53ef\u80fd\u7bc4\u570d &amp; =\u3000\u4e0b\u9650 \u81f3 \u4e0a\u9650 \u4e4b\u9593<br \/>\\end{align}<\/p><p>\u4f8b2\uff1a\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \u7528\u6700\u5c0f\u523b\u5ea6\u70ba0.1cm\u7684\u5c3a\u91cf\u5ea6\u66f8\u7684\u6ff6\u5ea6\uff0c\u91cf\u5ea6\u7d50\u679c\u662f\u5f9715cm\u3002<\/p><ul><li style=\"list-style-type: none;\"><ul><li>\u91cf\u5ea6\u503c = 15cm<\/li><li>\u6e96\u78ba\u5ea6 = 0.1cm<\/li><li>\u6700\u5927\u8aa4\u5dee = 0.1 \/ 2 = 0.05cm<\/li><li>\\(\u76f8\u5c0d\u8aa4\u5dee = \\dfrac{\u6700\u5927\u8aa4\u5dee}{\u91cf\u5ea6\u503c} = \\dfrac{0.05}{15} = \\dfrac{1}{300} \\)<\/li><li>\u767e\u5206\u8aa4\u5dee = \u76f8\u5c0d\u8aa4\u5dee \u00d7 100% = 0.33% (\u6e96\u78ba\u81f3\u4e8c\u4f4d\u6709\u6548\u6578\u5b57)<\/li><li>\u4e0a\u9650 = 15 \uff0b 0.05 = 15.05 cm<\/li><li>\u4e0b\u9650 = 15 \uff0d 0.05 = 14.95 cm<\/li><li>\u53ef\u80fd\u7bc4\u570d = 14.95 cm \u81f3 15.05 cm<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ef02d3a elementor-widget elementor-widget-text-editor\" data-id=\"ef02d3a\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p>\u76f8\u95dc\u8ab2\u984c\uff1a<\/p><ul><li>\u5047\u5982\u540c\u5b78\u5514\u4fc2\u597d\u660e\u4f9d\u8ab2\u8b1b\u5605\u5167\u5bb9\u3001\u5efa\u8b70\u91cd\u6eab\u300c<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/approximate-values-estimation\/\">\u8fd1\u4f3c\u503c\u8207\u4f30\u7b97<\/a>\u300d\u3002<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-9fee782 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9fee782\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-88b133a\" data-id=\"88b133a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-dfc83f7\" data-id=\"dfc83f7\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-d85fe33\" data-id=\"d85fe33\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-a8a05af elementor-widget elementor-widget-text-editor\" data-id=\"a8a05af\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/identities\/\">\u6046\u7b49\u5f0f <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-b556a13\" data-id=\"b556a13\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c1dd767 elementor-widget elementor-widget-sidebar\" data-id=\"c1dd767\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-3 > ul > li > a, .custom-menu-widget .ocean_custom_menu-3 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-3.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e8c\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-3 left dropdown-hover\"><ul id=\"menu-form2mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1248\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1248\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/approximation-errors\/\" class=\"menu-link\">1. \u8fd1\u4f3c\u8207\u8aa4\u5dee (Approximation &#038; Errors)<\/a><\/li>\n<li  id=\"menu-item-1261\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1261\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/identities\/\" class=\"menu-link\">2. \u6046\u7b49\u5f0f (Identities)<\/a><\/li>\n<li  id=\"menu-item-1266\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1266\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/factorization\/\" class=\"menu-link\">3. \u56e0\u5f0f\u5206\u89e3 (Factorization)<\/a><\/li>\n<li  id=\"menu-item-1265\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1265\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/formulae\/\" class=\"menu-link\">4. \u516c\u5f0f (Formulae)<\/a><\/li>\n<li  id=\"menu-item-1278\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1278\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/simultaneous-linear-equations\/\" class=\"menu-link\">5. \u806f\u7acb\u4e8c\u5143\u4e00\u6b21\u65b9\u7a0b (Simultaneous Linear Equations)<\/a><\/li>\n<li  id=\"menu-item-1279\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1279\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/rate-and-ratio\/\" class=\"menu-link\">6. \u7387\u53ca\u6bd4 (Rate and Ratio)<\/a><\/li>\n<li  id=\"menu-item-1280\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1280\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/use-of-percentage\/\" class=\"menu-link\">7. \u767e\u4efd\u6cd5 (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1302\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1302\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/geometry\/\" class=\"menu-link\">8. \u5e7e\u4f55\u5b9a\u7406 (Geometry)<\/a><\/li>\n<li  id=\"menu-item-1303\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1303\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/pythagoras-theorem\/\" class=\"menu-link\">9. \u7562\u6c0f\u5b9a\u7406 (Pythagoras\u2019 Theorem)<\/a><\/li>\n<li  id=\"menu-item-1304\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1304\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/trigonometric-ratios\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4 (Trigonometric Ratios)<\/a><\/li>\n<li  id=\"menu-item-1305\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1305\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/areas-and-volumes\/\" class=\"menu-link\">11. \u9762\u7a4d\u548c\u9ad4\u7a4d (Areas and Volumes)<\/a><\/li>\n<li  id=\"menu-item-1306\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1306\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form2_maths\/statistics\/\" class=\"menu-link\">12. \u7d71\u8a08 (Statistics)<\/a><\/li>\n<li  id=\"menu-item-16137\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16137\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>1.1\u00a0 \u6709\u6548\u6578\u5b57 (Significant Figure) \u6240\u8b02\u300c\u6709\u6548\u6578\u5b57\u300d\uff0c\u5176\u5be6\u4fc2\u53d6\u8fd1\u4f3c\u503c\u7684\u4e00\u500b\u65b9\u6cd5\u3002\u65e5\u5e38 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