{"id":81232,"date":"2021-03-31T12:10:55","date_gmt":"2021-03-31T06:40:55","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=81232"},"modified":"2022-04-01T10:26:33","modified_gmt":"2022-04-01T04:56:33","slug":"pemdas-rule-involving-decimals","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/pemdas-rule-involving-decimals\/","title":{"rendered":"PEMDAS Rule Involving Decimals &#8211; Definition, Examples | How to Solve PEMDAS?"},"content":{"rendered":"<p>PEMDAS Rule \u2013 Involving Decimals helps you to solve all the decimal operations easily in minutes. Improve your problem-solving skills using PEMDAS Rule while calculating decimal operations. The order of operations is also the same for the calculation of the decimal number using the PEMDAS Rule. The order of operations is Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. Check out different examples and also the order of operation in the below article.<\/p>\n<p>Do Refer:<\/p>\n<ul>\n<li><a href=\"https:\/\/ccssmathanswers.com\/pemdas-rule\/\">PEMDAS Rule<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/pemdas-rules-involving-integers\/\">PEMDAS Rules &#8211; Involving Integers<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/bodmas-rule\/\">BODMAS Rule<\/a><\/li>\n<\/ul>\n<h2>How to Solve PEMDAS(Order of Operations)?<\/h2>\n<p>1. Parenthesis Terms<br \/>\nWe have to give the first importance to the parenthesis terms while simplifying an arithmetic expression. For example<br \/>\n0.3 + (0.2 \u00d7 0.2).<br \/>\nIn the above, expression the parenthesis term is (0.2 \u00d7 0.2). By simplifying the term. We will get<br \/>\n0.3 + 0.04.<br \/>\n0.34 (addition).<\/p>\n<p>2. Exponent Terms<br \/>\nAfter solving the parenthesis terms, we have to give priority to exponent terms in the calculation. For example<br \/>\n0.5 \u00d7 (0.6 + 0.2) + (0.2)\u00b2.<br \/>\nFirst, simplify the parenthesis term. That is<br \/>\n0.5 \u00d7 0.8 + (0.2)\u00b2.<br \/>\nIn the above expression, the exponent term is (0.2)\u00b2. By simplifying the exponent term, we will get<br \/>\n0.5 \u00d7 0.8 + 0.04.<br \/>\n0.4 + 0.04 (Multiplication 0.5 \u00d7 0.8 = 0.4).<br \/>\n0.44 (addition).<\/p>\n<p>3. Multiplication Terms<br \/>\nWhile simplifying an arithmetic expression, we need to give the third priority for multiplication terms. For example<br \/>\n0.1 \u00d7 [(0.2 + 0.5) + (0.8 \u2013 0.4)] + (0.3 + 0.3)\u00b2.<br \/>\nSimplify the parenthesis terms. That is<br \/>\n0.1\u00d7[ 0.7 + 0.4 ] + (0.6)\u00b2.<br \/>\n0.1\u00d71.1 + (0.6)\u00b2. (again Parenthesis term simplification).<br \/>\nNext, simplify the Exponent terms. That is<br \/>\n0.1\u00d7 1.1 + 0.36.<br \/>\nNow, simplify the Multiplication term 0.1\u00d7 1.1. we will get<br \/>\n0.11 + 0.36 = 0.47.<\/p>\n<p>4. Division Simplification.<br \/>\nThe next priority while simplification of expression is division terms. For example<br \/>\n0.3 \u00d7 (0.25 + 0.12) \u00f7 0.1 + (0.24)\u00b2.<br \/>\nFirst, simplify the parenthesis terms. That is<br \/>\n0.3 \u00d7 0.37 \u00f7 0.1 + (0.24)\u00b2.<br \/>\nThe second priority for exponent terms. That is<br \/>\n0.3 \u00d7 0.37 \u00f7 0.1 + 0.0576.<br \/>\nSimplify the Multiplication Terms. That is<br \/>\n0.111 \u00f7 0.1 + 0.0576.<br \/>\nNow, Simplify the division terms. We will get<br \/>\n1.11 + 0.0576.<br \/>\n1.1676.<\/p>\n<p>5. Addition Terms Simplification.<br \/>\nThe fifth priority while calculating an arithmetic expression is addition terms. For example<br \/>\n0.5 + 0.25 \u00f7 0.1 + (0.8)\u00b2 + (0.2 + 0.6).<br \/>\nSimplify the parenthesis terms. We will get<br \/>\n0.5 + 0.25 \u00f7 0.1 + (0.8)\u00b2 + 0.8.<br \/>\nExponent terms simplification.<br \/>\n0.5 + 0.25 \u00f7 0.1 + 0.64 + 0.8.<br \/>\nDivision terms simplification.<br \/>\n0.5 + 2.5 + 0.64 + 0.8.<br \/>\nNow, simplify the additional terms. That is<br \/>\n1.44.<\/p>\n<p>6. Subtraction Terms Simplification.<br \/>\nThe last priority while the simplification process is subtraction. For example<br \/>\n0.4 + (0.2)\u00b3 \u00d7 0.1 \u00f7 0.2 &#8211; 0.25.<br \/>\nSimplify the exponent terms first. That is<br \/>\n0.4 + 0.008\u00d7 0.1 \u00f7 0.2 &#8211; 0.25.<br \/>\nMultiplication terms simplification.<br \/>\n0.4 + 0.0008 \u00f7 0.2 &#8211; 0.25.<br \/>\nSimplify the division terms.<br \/>\n0.4 + 0.004 &#8211; 0.25.<br \/>\nAddition terms simplification.<br \/>\n0.404 \u2013 0.25.<br \/>\nSubtraction simplification.<br \/>\n0.154.<\/p>\n<h3>PEMDAS Rule Involving Decimals Worked Out Problems<\/h3>\n<p>1. Simplify the given expressions by using the PEMDAS Rule<br \/>\n(i) 10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + (0.4 + 0.6).<br \/>\n(ii) 12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + (1.25 \u2013 0.2).<br \/>\n(iii) 20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 (0.3)\u00b2.<br \/>\n(iv) 50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.2 \u2013 0.1)\u00b3.<\/p>\n<p>(i) 10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + (0.4 + 0.6).<\/p>\n<p>Solution:<\/p>\n<p>The given expression is 10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + (0.4 + 0.6).<br \/>\nAs per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.<br \/>\n10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + (0.4 + 0.6).<br \/>\n10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + 1.<br \/>\n10.5 \u2013 0.5 \u00d7 0.25 + 0.25 + 1.<br \/>\n10.5 \u20130.125 + 0.25 + 1.<br \/>\n11.75 \u2013 0.125.<br \/>\n11.625.<br \/>\nBy simplifying the expression 10.5 \u2013 0.5 \u00d7 0.25 + (0.5)\u00b2 + (0.4 + 0.6), we will get the resultant value as 11.625.<\/p>\n<p>(ii) 12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + (1.25 \u2013 0.2).<\/p>\n<p>Solution:<\/p>\n<p>The given expression is 12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + (1.25 \u2013 0.2).<br \/>\nAs per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.<br \/>\n12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + (1.25 \u2013 0.2).<br \/>\n12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + 1.05.<br \/>\n12.5 + 0.138 \u2013 0.89 + 1.05.<br \/>\n13.688 \u2013 0.89.<br \/>\n12.798.<br \/>\nBy simplifying the expression 12.5 + 0.6 \u00d7 0.23 \u2013 0.89 + (1.25 \u2013 0.2)<br \/>\nwe will get the resultant value as 12.798.<\/p>\n<p>(iii) 20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 (0.3)\u00b2.<\/p>\n<p>Solution:<\/p>\n<p>The given expression is 20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 (0.3)\u00b2.<br \/>\nAs per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.<br \/>\n20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 (0.3)\u00b2.<br \/>\n20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 0.09.<br \/>\n20.25 \u00f7 0.5 + 0.26 \u2013 0.5805.<br \/>\n40.5 + 0.26 \u2013 0.5805.<br \/>\n40.76 \u2013 0.5805.<br \/>\n40.1795.<br \/>\nBy simplifying the expression 20.25 \u00f7 0.5 + 0.26 \u2013 6.45 \u00d7 (0.3)\u00b2<br \/>\nwe will get the resultant value as 40.1795.<\/p>\n<p>(iv) 50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.2 \u2013 0.1)\u00b3.<\/p>\n<p>Solution:<\/p>\n<p>The given expression is 50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.2 \u2013 0.1)\u00b3.<br \/>\nAs per the PEMDAS rule, we have to follow the order of operations while simplifying the expression. That is, Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction.<br \/>\n50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.2 \u2013 0.1)\u00b3.<br \/>\n50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.1)\u00b3.<br \/>\n50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + 0.001.<br \/>\n50.6 \u2013 11.34 + 0.5 + 0.001.<br \/>\n51.101 \u2013 11.34.<br \/>\n39.761.<br \/>\nBy simplifying the expression 50.6 \u2013 25.2 \u00d7 0.45 + 0.5 + (0.2 \u2013 0.1)\u00b3 we will get the resultant value as 39.761.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>PEMDAS Rule \u2013 Involving Decimals helps you to solve all the decimal operations easily in minutes. Improve your problem-solving skills using PEMDAS Rule while calculating decimal operations. The order of operations is also the same for the calculation of the decimal number using the PEMDAS Rule. 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