{"id":8317,"date":"2023-09-29T14:37:44","date_gmt":"2023-09-29T14:37:44","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=8317"},"modified":"2025-08-29T20:30:24","modified_gmt":"2025-08-29T20:30:24","slug":"math-in-arts-common-scenarios-background-youll-need-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/math-in-arts-common-scenarios-background-youll-need-1\/","title":{"raw":"Math in Arts - Common Scenarios: Background You'll Need 1","rendered":"Math in Arts &#8211; Common Scenarios: Background You&#8217;ll Need 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Convert between decimals and fractions<\/li>\r\n<\/ul>\r\n<\/section>\r\n<h2>Write a Decimal as a Fraction<\/h2>\r\n<p>We often need to rewrite decimals as fractions or mixed numbers. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\\text{\\$3.45}[\/latex] , the bottle of water costs [latex]\\text{\\$1.25}[\/latex] , and the total sales tax is [latex]\\text{\\$0.33}[\/latex] , what is the total cost of your lunch?<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"177\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221427\/CNX_BMath_Figure_05_01_002_img.png\" alt=\"A vertical addition problem. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" width=\"177\" height=\"83\" \/> Figure 1. The total cost of lunch[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>The total is [latex]$5.03[\/latex]. Suppose you pay with a [latex]$5[\/latex] bill and [latex]3[\/latex] pennies. Should you wait for change? No, [latex]\\text{\\$5}[\/latex] and [latex]3[\/latex] pennies is the same as [latex]\\text{\\$5.03}[\/latex].<\/p>\r\n<p>Because [latex]\\text{100 pennies}=\\text{\\$1}[\/latex], each penny is worth [latex]{\\Large\\frac{1}{100}}[\/latex] of a dollar. We write the value of one penny as [latex]$0.01[\/latex], since [latex]0.01={\\Large\\frac{1}{100}}[\/latex].<\/p>\r\n<p>Let\u2019s see how we can convert decimal numbers to fractions. We know that [latex]$5.03[\/latex] means [latex]5[\/latex] dollars and [latex]3[\/latex] cents. Since there are [latex]100[\/latex] cents in one dollar, [latex]3[\/latex] cents means [latex]{\\Large\\frac{3}{100}}[\/latex] of a dollar, so [latex]0.03={\\Large\\frac{3}{100}}[\/latex].<\/p>\r\n<p>We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[\/latex], the [latex]3[\/latex] is in the hundredths place, so [latex]100[\/latex] is the denominator of the fraction equivalent to [latex]0.03[\/latex].<\/p>\r\n<p style=\"text-align: center;\">[latex]0.03={\\Large\\frac{3}{100}}[\/latex]<\/p>\r\n<p>For our [latex]$5.03[\/latex] lunch, we can write the decimal [latex]5.03[\/latex] as a mixed number.<\/p>\r\n<p style=\"text-align: center;\">[latex]5.03=5{\\Large\\frac{3}{100}}[\/latex]<\/p>\r\n<p>Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><b>How To: Convert a Decimal Number to a Fraction or Mixed Number<\/b><\/p>\r\n<ol id=\"eip-id1168468271407\" class=\"stepwise\">\r\n\t<li>Look at the number to the left of the decimal.<br \/>\r\n<ul id=\"eip-id1168468271412\">\r\n\t<li>If it is zero, the decimal converts to a proper fraction.<\/li>\r\n\t<li>If it is not zero, the decimal converts to a mixed number.<br \/>\r\n<ul id=\"eip-id1168468449219\">\r\n\t<li>Write the whole number.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Determine the place value of the final digit.<\/li>\r\n\t<li>Write the fraction.<br \/>\r\n<ul id=\"eip-id1168468484466\">\r\n\t<li>numerator\u2014the \u2018numbers\u2019 to the right of the decimal point<\/li>\r\n\t<li>denominator\u2014the place value corresponding to the final digit<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Simplify the fraction, if possible.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6763[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Convert between decimals and fractions<\/li>\n<\/ul>\n<\/section>\n<h2>Write a Decimal as a Fraction<\/h2>\n<p>We often need to rewrite decimals as fractions or mixed numbers. Suppose you buy a sandwich and a bottle of water for lunch. If the sandwich costs [latex]\\text{\\$3.45}[\/latex] , the bottle of water costs [latex]\\text{\\$1.25}[\/latex] , and the total sales tax is [latex]\\text{\\$0.33}[\/latex] , what is the total cost of your lunch?<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 177px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221427\/CNX_BMath_Figure_05_01_002_img.png\" alt=\"A vertical addition problem. The top line shows $3.45 for a sandwich, the next line shows $1.25 for water, and the last line shows $0.33 for tax. The total is shown to be $5.03.\" width=\"177\" height=\"83\" \/><figcaption class=\"wp-caption-text\">Figure 1. The total cost of lunch<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The total is [latex]$5.03[\/latex]. Suppose you pay with a [latex]$5[\/latex] bill and [latex]3[\/latex] pennies. Should you wait for change? No, [latex]\\text{\\$5}[\/latex] and [latex]3[\/latex] pennies is the same as [latex]\\text{\\$5.03}[\/latex].<\/p>\n<p>Because [latex]\\text{100 pennies}=\\text{\\$1}[\/latex], each penny is worth [latex]{\\Large\\frac{1}{100}}[\/latex] of a dollar. We write the value of one penny as [latex]$0.01[\/latex], since [latex]0.01={\\Large\\frac{1}{100}}[\/latex].<\/p>\n<p>Let\u2019s see how we can convert decimal numbers to fractions. We know that [latex]$5.03[\/latex] means [latex]5[\/latex] dollars and [latex]3[\/latex] cents. Since there are [latex]100[\/latex] cents in one dollar, [latex]3[\/latex] cents means [latex]{\\Large\\frac{3}{100}}[\/latex] of a dollar, so [latex]0.03={\\Large\\frac{3}{100}}[\/latex].<\/p>\n<p>We convert decimals to fractions by identifying the place value of the farthest right digit. In the decimal [latex]0.03[\/latex], the [latex]3[\/latex] is in the hundredths place, so [latex]100[\/latex] is the denominator of the fraction equivalent to [latex]0.03[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]0.03={\\Large\\frac{3}{100}}[\/latex]<\/p>\n<p>For our [latex]$5.03[\/latex] lunch, we can write the decimal [latex]5.03[\/latex] as a mixed number.<\/p>\n<p style=\"text-align: center;\">[latex]5.03=5{\\Large\\frac{3}{100}}[\/latex]<\/p>\n<p>Notice that when the number to the left of the decimal is zero, we get a proper fraction. When the number to the left of the decimal is not zero, we get a mixed number.<\/p>\n<section class=\"textbox questionHelp\">\n<p><b>How To: Convert a Decimal Number to a Fraction or Mixed Number<\/b><\/p>\n<ol id=\"eip-id1168468271407\" class=\"stepwise\">\n<li>Look at the number to the left of the decimal.\n<ul id=\"eip-id1168468271412\">\n<li>If it is zero, the decimal converts to a proper fraction.<\/li>\n<li>If it is not zero, the decimal converts to a mixed number.\n<ul id=\"eip-id1168468449219\">\n<li>Write the whole number.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li>Determine the place value of the final digit.<\/li>\n<li>Write the fraction.\n<ul id=\"eip-id1168468484466\">\n<li>numerator\u2014the \u2018numbers\u2019 to the right of the decimal point<\/li>\n<li>denominator\u2014the place value corresponding to the final digit<\/li>\n<\/ul>\n<\/li>\n<li>Simplify the fraction, if possible.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6763\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6763&theme=lumen&iframe_resize_id=ohm6763&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":2,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":8095,"module-header":"background_you_need","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8317"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":8,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8317\/revisions"}],"predecessor-version":[{"id":15937,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8317\/revisions\/15937"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/8095"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/8317\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=8317"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=8317"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=8317"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=8317"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}