{"id":1055,"date":"2023-03-29T15:34:55","date_gmt":"2023-03-29T15:34:55","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=1055"},"modified":"2025-08-24T04:04:14","modified_gmt":"2025-08-24T04:04:14","slug":"decimals-learn-it-1","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/decimals-learn-it-1\/","title":{"raw":"Decimals: Learn It 1","rendered":"Decimals: Learn It 1"},"content":{"raw":"<section class=\"textbox learningGoals\">\r\n<ul>\r\n\t<li>Write and name decimals<\/li>\r\n\t<li>Turn a decimal into a fraction<\/li>\r\n\t<li>Place decimals on a number line and order them<\/li>\r\n\t<li>Solve equations using decimals<\/li>\r\n<\/ul>\r\n<\/section>\r\n<p>You probably already know quite a bit about decimals based on your experience with money. 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. Add the prices for the sandwich, water, and tax to get $5.03 total[\/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>Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, <strong>decimals<\/strong> are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten.<\/p>\r\n<section class=\"textbox keyTakeaway\">\r\n<div>\r\n<h3>decimals<\/h3>\r\n<p><strong>Decimals<\/strong> represent fractions or parts of a whole, based on powers of ten, using a point known as a decimal point. They provide a way to express numbers between whole numbers and allow for accurate representation of values, especially in measurement and calculations.<\/p>\r\n<\/div>\r\n<\/section>\r\n<p>How are decimals related to fractions? The table below\u00a0shows the relation.<\/p>\r\n<table id=\"fs-id2474612\" summary=\"A table is shown with three columns and five rows. The first row is a header row and it labels each column, \">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th>Decimal<\/th>\r\n<th>Fraction<\/th>\r\n<th>Name<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>[latex]0.1[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{10}}[\/latex]<\/td>\r\n<td>One tenth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.01[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{100}}[\/latex]<\/td>\r\n<td>One hundredth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.001[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{1,000}}[\/latex]<\/td>\r\n<td>One thousandth<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>[latex]0.0001[\/latex]<\/td>\r\n<td>[latex]{\\Large\\frac{1}{10,000}}[\/latex]<\/td>\r\n<td>One ten-thousandth<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p>&nbsp;<\/p>\r\n<p>When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read [latex]10,000[\/latex] as <em>ten thousand<\/em>. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in the\u00a0first table\u00a0relate to the names of the fractions from the second table.<\/p>\r\n<p>This chart illustrates place values to the left and right of the decimal point.<\/p>\r\n<center>\r\n[caption id=\"\" align=\"aligncenter\" width=\"189\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/277\/2017\/04\/24221429\/CNX_BMath_Figure_05_01_002.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=\"189\" height=\"86\" \/> Figure 2. Place values on the left and right of the decimal[\/caption]\r\n<\/center>\r\n<p>&nbsp;<\/p>\r\n<p>Notice two important facts shown in the tables.<\/p>\r\n<ul id=\"fs-id1852418\">\r\n\t<li>The \"th\" at the end of the name means the number is a fraction. \"One thousand\" is a number larger than one, but \"one thousandth\" is a number smaller than one.<\/li>\r\n\t<li>The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.<\/li>\r\n<\/ul>\r\n<p>Remember that [latex]$5.03[\/latex] lunch? We read [latex]$5.03[\/latex] as <em>five dollars and three cents<\/em>. Naming decimals (those that don\u2019t represent money) is done in a similar way. We read the number [latex]5.03[\/latex] as <em>five and three hundredths<\/em>.<\/p>\r\n<p>We sometimes need to translate a number written in decimal notation into words.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Name a Decimal Number<\/strong><\/p>\r\n<ol>\r\n\t<li>Name the number to the left of the decimal point.<\/li>\r\n\t<li>Write \"and\" for the decimal point.<\/li>\r\n\t<li>Name the \"number\" part to the right of the decimal point as if it were a whole number.<\/li>\r\n\t<li>Name the decimal place of the last digit.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6677[\/ohm2_question]<\/section>\r\n<p>Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.<\/p>\r\n<section class=\"textbox questionHelp\">\r\n<p><strong>How To: Write a Decimal Number From Its Name<\/strong><\/p>\r\n<ol id=\"eip-id1168468315974\" class=\"stepwise\">\r\n\t<li>Look for the word \"and\"\u2014it locates the decimal point.<\/li>\r\n\t<li>Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.<br \/>\r\n<ul id=\"eip-id1168468368974\">\r\n\t<li>Place a decimal point under the word \"and.\" Translate the words before \"and\" into the whole number and place it to the left of the decimal point.<\/li>\r\n\t<li>If there is no \"and,\" write a \"[latex]0[\/latex]\" with a decimal point to its right.<\/li>\r\n<\/ul>\r\n<\/li>\r\n\t<li>Translate the words after \"and\" into the number to the right of the decimal point. Write the number in the spaces\u2014putting the final digit in the last place.<\/li>\r\n\t<li>Fill in zeros for place holders as needed.<\/li>\r\n<\/ol>\r\n<\/section>\r\n<section class=\"textbox tryIt\">[ohm2_question hide_question_numbers=1]6734[\/ohm2_question]<\/section>","rendered":"<section class=\"textbox learningGoals\">\n<ul>\n<li>Write and name decimals<\/li>\n<li>Turn a decimal into a fraction<\/li>\n<li>Place decimals on a number line and order them<\/li>\n<li>Solve equations using decimals<\/li>\n<\/ul>\n<\/section>\n<p>You probably already know quite a bit about decimals based on your experience with money. 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. Add the prices for the sandwich, water, and tax to get $5.03 total<\/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>Writing a number with a decimal is known as decimal notation. It is a way of showing parts of a whole when the whole is a power of ten. In other words, <strong>decimals<\/strong> are another way of writing fractions whose denominators are powers of ten. Just as the counting numbers are based on powers of ten, decimals are based on powers of ten.<\/p>\n<section class=\"textbox keyTakeaway\">\n<div>\n<h3>decimals<\/h3>\n<p><strong>Decimals<\/strong> represent fractions or parts of a whole, based on powers of ten, using a point known as a decimal point. They provide a way to express numbers between whole numbers and allow for accurate representation of values, especially in measurement and calculations.<\/p>\n<\/div>\n<\/section>\n<p>How are decimals related to fractions? The table below\u00a0shows the relation.<\/p>\n<table id=\"fs-id2474612\" summary=\"A table is shown with three columns and five rows. The first row is a header row and it labels each column,\">\n<thead>\n<tr valign=\"top\">\n<th>Decimal<\/th>\n<th>Fraction<\/th>\n<th>Name<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>[latex]0.1[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{10}}[\/latex]<\/td>\n<td>One tenth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.01[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{100}}[\/latex]<\/td>\n<td>One hundredth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.001[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{1,000}}[\/latex]<\/td>\n<td>One thousandth<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>[latex]0.0001[\/latex]<\/td>\n<td>[latex]{\\Large\\frac{1}{10,000}}[\/latex]<\/td>\n<td>One ten-thousandth<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p>When we name a whole number, the name corresponds to the place value based on the powers of ten. In Whole Numbers, we learned to read [latex]10,000[\/latex] as <em>ten thousand<\/em>. Likewise, the names of the decimal places correspond to their fraction values. Notice how the place value names in the\u00a0first table\u00a0relate to the names of the fractions from the second table.<\/p>\n<p>This chart illustrates place values to the left and right of the decimal point.<\/p>\n<div style=\"text-align: center;\">\n<figure style=\"width: 189px\" 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\/24221429\/CNX_BMath_Figure_05_01_002.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=\"189\" height=\"86\" \/><figcaption class=\"wp-caption-text\">Figure 2. Place values on the left and right of the decimal<\/figcaption><\/figure>\n<\/div>\n<p>&nbsp;<\/p>\n<p>Notice two important facts shown in the tables.<\/p>\n<ul id=\"fs-id1852418\">\n<li>The &#8220;th&#8221; at the end of the name means the number is a fraction. &#8220;One thousand&#8221; is a number larger than one, but &#8220;one thousandth&#8221; is a number smaller than one.<\/li>\n<li>The tenths place is the first place to the right of the decimal, but the tens place is two places to the left of the decimal.<\/li>\n<\/ul>\n<p>Remember that [latex]$5.03[\/latex] lunch? We read [latex]$5.03[\/latex] as <em>five dollars and three cents<\/em>. Naming decimals (those that don\u2019t represent money) is done in a similar way. We read the number [latex]5.03[\/latex] as <em>five and three hundredths<\/em>.<\/p>\n<p>We sometimes need to translate a number written in decimal notation into words.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Name a Decimal Number<\/strong><\/p>\n<ol>\n<li>Name the number to the left of the decimal point.<\/li>\n<li>Write &#8220;and&#8221; for the decimal point.<\/li>\n<li>Name the &#8220;number&#8221; part to the right of the decimal point as if it were a whole number.<\/li>\n<li>Name the decimal place of the last digit.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6677\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6677&theme=lumen&iframe_resize_id=ohm6677&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n<p>Now we will translate the name of a decimal number into decimal notation. We will reverse the procedure we just used.<\/p>\n<section class=\"textbox questionHelp\">\n<p><strong>How To: Write a Decimal Number From Its Name<\/strong><\/p>\n<ol id=\"eip-id1168468315974\" class=\"stepwise\">\n<li>Look for the word &#8220;and&#8221;\u2014it locates the decimal point.<\/li>\n<li>Mark the number of decimal places needed to the right of the decimal point by noting the place value indicated by the last word.\n<ul id=\"eip-id1168468368974\">\n<li>Place a decimal point under the word &#8220;and.&#8221; Translate the words before &#8220;and&#8221; into the whole number and place it to the left of the decimal point.<\/li>\n<li>If there is no &#8220;and,&#8221; write a &#8220;[latex]0[\/latex]&#8221; with a decimal point to its right.<\/li>\n<\/ul>\n<\/li>\n<li>Translate the words after &#8220;and&#8221; into the number to the right of the decimal point. Write the number in the spaces\u2014putting the final digit in the last place.<\/li>\n<li>Fill in zeros for place holders as needed.<\/li>\n<\/ol>\n<\/section>\n<section class=\"textbox tryIt\"><iframe loading=\"lazy\" id=\"ohm6734\" class=\"resizable\" src=\"https:\/\/ohm.one.lumenlearning.com\/multiembedq.php?id=6734&theme=lumen&iframe_resize_id=ohm6734&source=tnh\" width=\"100%\" height=\"150\"><\/iframe><\/section>\n","protected":false},"author":15,"menu_order":4,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc-attribution\",\"description\":\"Prealgebra\",\"author\":\"Lynn Marecek & MaryAnne Anthony-Smith\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/prealgebra\/pages\/5-1-decimals\",\"project\":\"5.1 Decimals\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757\"}]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":54,"module-header":"learn_it","content_attributions":[{"type":"cc-attribution","description":"Prealgebra","author":"Lynn Marecek & MaryAnne Anthony-Smith","organization":"OpenStax","url":"https:\/\/openstax.org\/books\/prealgebra\/pages\/5-1-decimals","project":"5.1 Decimals","license":"cc-by","license_terms":"Access for free at http:\/\/cnx.org\/contents\/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757"}],"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\/1055"}],"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":24,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1055\/revisions"}],"predecessor-version":[{"id":15599,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1055\/revisions\/15599"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/54"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/1055\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=1055"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=1055"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=1055"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=1055"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}