[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-563251-105":53,"doc-detail-563251-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","decimals-introduction-to-meaning-place-value-and-rounding","Decimals - Introduction to Meaning, Place Value, and Rounding","","Decimals explains what decimal numbers represent in a base-10 system, linking each digit’s position to place value and showing how the decimal point separates the whole-number part from the fractional part. It demonstrates multiplication and division by powers of ten using a place-value chart, including the role of placeholders. It then covers converting between decimals and fractions and rounding to specified decimal places or significant figures, with an overview of irrational numbers.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/decimals-introduction-to-meaning-place-value-and-rounding/563251/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/decimals-introduction-to-meaning-place-value-and-rounding/563251.png","ImageObject",442,249,{"name":88,"@type":89},"dawugda","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-31","2026-10-12",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",9,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What does the decimal system use to represent numbers?","Question",{"text":109,"@type":110},"It uses digits 0–9, placing them in different positions to express values from very small to very large, with the decimal point indicating where the fractional part begins.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How does multiplying by powers of ten affect a decimal?",{"text":114,"@type":110},"Digits shift left on the place-value chart as multiplication by ten makes each moved digit ten times larger, and empty positions are filled with zeros where needed.",{"name":116,"@type":107,"acceptedAnswer":117},"How can a decimal be rounded?",{"text":118,"@type":110},"A decimal can be rounded to a chosen number of decimal places or to a chosen number of significant figures, controlling the accuracy of the final value.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},563251,1792081904,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":136,"language":137,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":61,"update_tm":141,"read_time":76},3985747870947,"https://ap-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Decimals  \nmc-TY-decimals-2009-1  \nIn this unit we shall look at the meaning of decimals, and how they are related to fractions. We shall then look at rounding to given numbers of decimal places or significant figures. Finally we shall take a brief look at irrational numbers.  \nIn order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature.  \nAfter reading this text, and/or viewing the video tutorial on this topic, you should be able to:  \n• multiply and divide a decimal by powers of ten;  \n• convert decimals into fractions, and vice versa;  \n• round a decimal number to a given number of decimal places, or to a given number of significant figures.  \nContents  \n1. Introduction 2  \n2. Multiplying and dividing by ten 3  \n3. Decimals and fractions 4  \n4. The accuracy of decimals 6  \n5. Irrational numbers 7  \n[www.mathcentre.ac.uk 1](www.mathcentre.ac.uk 1) 􀀍c mathcentre 2009   \n1. Introduction  \nA simple meaning of the word ‘decimal’ is ‘connected with ten’, and the decimal number system is a means of expressing any number from the very smallest to the very largest.  \nLet us look at how the system works. We have the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9, they are our units, or ‘ones’. To make all our other numbers we use these same digits, but in different places in our decimal system. For example, in the number 12, ‘2’ is in the units place and stands for 2 units, and ‘1’ is in the tens place and stands for one times ten, giving us 2 + 10 = 12 .  \nWe can describe this by using a place value chart, and labelling the columns.  \n\n| 1000000 | 100000 | 10000 | 1000 | 100 | 10 | 1 • | 1/10 | 1/100 | 1/1000 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  |  |  |  |  |  |\n\nThe decimal point shows us where the fraction part of a number begins. To the left of the decimal point we have the whole number part. We have the units, the tens, hundreds, thousands, ten thousands, hundred thousands, millions and so on. You can see that, as we go from right to left, each column heading is ten times larger than its neighbour, so going in this direction weare multiplying by ten each time. On the other hand, if we go from left to right, each column  \nheading is ten times smaller than its neighbour, so going in this direction we are dividing by ten. To the right of the decimal point we have the fractional part of the number. If we continue going right, we continue dividing by ten. So we get tenths, hundredths, thousandths and so on. We can put some numbers in the chart.  \n\n| 1000000 | 100000 | 10000 | 1000 | 100 | 10 | 1 • | 1/10 | 1/100 | 1/1000 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 2 | 7 |  |  |  |\n|  |  |  |  | 5 | 3 | 1 |  |  |  |\n|  |  |  |  |  | 5 | 0 |  |  |  |\n|  |  |  | 6 | 0 | 0 | 0 |  |  |  |\n|  |  |  |  | 2 | 0 | 7 |  |  |  |\n|  | 1 | 2 | 7 | 3 | 9 | 5 |  |  |  |\n|  |  |  |  |  |  | 6 | • 3 | 9 | 2 |\n|  |  |  |  |  |  | 0 | • 5 |  |  |\n|  |  |  |  |  | 1 | 2 | • 0 | 2 | 7 |\n\nThese numbers are 27, 531, 50, 6 000 , 207, 127 395, 6 .392, 0 .5, and 12 .027. In the chart, the numbers are aligned so that the units are vertically above or below one another, and similarly for the tens, the hundreds, and so on. For instance, 50 has a 5 in the tens column. But we also put a 0 in the units column, to show that there are no units. This 0 is called a ‘placeholder’, because it makes sure we realise that the 5 represents 5 tens, and not 5 units.  \n[www.mathcentre.ac.uk 2](www.mathcentre.ac.uk 2) 􀀍c mathcentre 2009   \n2. Multiplying and dividing by ten  \nUsing our chart, we can see what happens when we multiply a number by ten. We shall workout 34 × 10.  \n\n| 1000000 | 100000 | 10000 | 1000 | 100 | 10 | 1 • | 1/10 | 1/100 | 1/1000 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n|  |  |  |  |  | 3 | 4 |  |  |  |\n|  |  |  |  | ւ | ւ |  |  |  |  |\n|  |  |  |  | 3 | 4 | 0 |  |  |  |\n\nThe 3 representi","cbCaijszlSL9YhpQ","https://ap.wps.com/l/cbCaijszlSL9YhpQ","pdf",184413,8,"English","# Introduction\n# Multiplying and dividing by ten\n# Decimals and fractions\n# The accuracy of decimals\n# Irrational numbers","[{\"question\":\"What does the decimal system use to represent numbers?\",\"answer\":\"It uses digits 0–9, placing them in different positions to express values from very small to very large, with the decimal point indicating where the fractional part begins.\"},{\"question\":\"How does multiplying by powers of ten affect a decimal?\",\"answer\":\"Digits shift left on the place-value chart as multiplication by ten makes each moved digit ten times larger, and empty positions are filled with zeros where needed.\"},{\"question\":\"How can a decimal be rounded?\",\"answer\":\"A decimal can be rounded to a chosen number of decimal places or to a chosen number of significant figures, controlling the accuracy of the final value.\"}]","Decimals - Introduction to Meaning, Place Value, and Rounding | PDF",1791823702]