{"id":213614,"date":"2024-02-15T11:54:46","date_gmt":"2024-02-15T17:54:46","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=213614"},"modified":"2026-03-30T15:40:17","modified_gmt":"2026-03-30T20:40:17","slug":"decimal-calculator","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/decimal-calculator\/","title":{"rendered":"Decimal Calculator"},"content":{"rendered":"<p>Use this calculator to perform an operation on any two decimal numbers. Select from the dropdown menu to add, subtract, multiply, divide, or even more.<\/p>\n<div class=\"decc-wrap\">\n<div class=\"decc-calculator\">\n<div class=\"decc-body\">\n<div class=\"decc-input-fields\">\n<div class=\"decc-input-row\" id=\"decc-dec1Row\">\n<div class=\"decc-input-label\">a<\/div>\n<p>          <input type=\"text\" id=\"decc-dec1Input\" placeholder=\"Decimal a\" onfocus=\"deccClearError('decc-dec1Row')\" oninput=\"deccCalculate()\">\n        <\/div>\n<div class=\"decc-input-row\" id=\"decc-dec2Row\">\n<div class=\"decc-input-label\">b<\/div>\n<p>          <input type=\"text\" id=\"decc-dec2Input\" placeholder=\"Decimal b\" onfocus=\"deccClearError('decc-dec2Row')\" oninput=\"deccCalculate()\">\n        <\/div>\n<div class=\"decc-dropdown-row\">\n<div class=\"decc-dropdown-label\" id=\"decc-opSymbol\">+<\/div>\n<p>          <select id=\"decc-dropdown\" onchange=\"deccCalculate()\"><option value=\"Add\">Add<\/option><option value=\"Subtract\">Subtract<\/option><option value=\"Multiply\">Multiply<\/option><option value=\"Divide\">Divide<\/option><option value=\"Exponent\">Exponent<\/option><option value=\"Root\">Root<\/option><option value=\"Logarithm\">Logarithm<\/option><\/select>\n        <\/div>\n<\/p><\/div>\n<div class=\"decc-formula\" id=\"decc-formula\"><math><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><mo>=<\/mo><mo>?<\/mo><\/math><\/div>\n<div class=\"decc-result-value\" id=\"decc-result\"><span class=\"decc-result-placeholder\"><\/span><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/div>\n<p style=\"text-align: center; margin-bottom: 3em; margin-top: 0.7em; font-size: 80%;\">Found a bug? <a class=\"ylist\" href=\"https:\/\/airtable.com\/appgcc1PP0BbzPCbI\/shrb33jgGwb66DWHC?prefill_Test=Decimal%20Calculator&#038;prefill_Question+Number=0&#038;prefill_Which+Form=Calculator-Feedback&#038;prefill_UP-ID=Calculator-Feedback%20-%20Decimal%20Calculator%20-%200&#038;hide_Test=true&#038;hide_Which+Form=true&#038;hide_UP-ID=true&#038;hide_Question+Number=true\" target=\"_blank\" rel=\"noopener\">Let us know!<\/a><\/p>\n<h2><span id=\"Adding_Decimals\" class=\"m-toc-anchor\"><\/span>Adding Decimals<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Add \\(5.8 + 2.35\\)<\/div>\n<p>To add decimals, you line up the decimal points and add the numbers as you normally would. Go from right to left, column by column.<\/p>\n<p>For \\(5.8 + 2.35\\), let&#8217;s first line up the decimal points. If a number doesn&#8217;t have as many decimal places as the other, you can add one or more zeroes to the end.<\/p>\n<p><math display=\"block\">\n  <mtable columnalign=\"right right center right\"\n          columnspacing=\"0.5em 0.08em 0.08em 0em\"\n          rowlines=\"none solid\">\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>5<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>80<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><mo>+<\/mo><\/mtd>\n      <mtd><mn>2<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>35<\/mn><\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>Now, we just add the columns, starting from the right. Be sure to carry over when necessary.<\/p>\n<p><math display=\"block\">\n  <mtable columnalign=\"right right center right\"\n          columnspacing=\"0.5em 0.08em 0.08em 0em\"\n          rowlines=\"none solid\">\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>5<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>80<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><mo>+<\/mo><\/mtd>\n      <mtd><mn>2<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>35<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>8<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>15<\/mn><\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>Therefore, \\(5.8+2.35=8.15\\)!<\/p>\n<hr \/>\n<h2><span id=\"Subtracting_Decimals\" class=\"m-toc-anchor\"><\/span>Subtracting Decimals<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Subtract \\(9.5 &#8211; 3.25\\)<\/div>\n<p>Subtracting decimals works just like adding. You line up the decimal points and subtract as you would with whole numbers.<\/p>\n<p>For \\(9.5 &#8211; 3.25\\), let&#8217;s first line up the decimal points. Remember, we can add trailing zeroes to make the numbers the same length after the decimal point.<\/p>\n<p><math display=\"block\">\n  <mtable columnalign=\"right right center right\"\n          columnspacing=\"0.5em 0.08em 0.08em 0em\"\n          rowlines=\"none solid\">\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>9<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>50<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><mo>&#8211;<\/mo><\/mtd>\n      <mtd><mn>3<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>25<\/mn><\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>Then, subtract the columns, borrowing from the next column as you go if needed.<\/p>\n<p><math display=\"block\">\n  <mtable columnalign=\"right right center right\"\n          columnspacing=\"0.5em 0.08em 0.08em 0em\"\n          rowlines=\"none solid\">\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>9<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>50<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><mo>&#8211;<\/mo><\/mtd>\n      <mtd><mn>3<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>25<\/mn><\/mtd>\n    <\/mtr>\n    <mtr>\n      <mtd><\/mtd>\n      <mtd><mn>6<\/mn><\/mtd>\n      <mtd><mo>.<\/mo><\/mtd>\n      <mtd><mn>25<\/mn><\/mtd>\n    <\/mtr>\n  <\/mtable>\n<\/math><\/p>\n<p>Therefore, \\(9.5 &#8211; 3.25=6.25\\)!<\/p>\n<hr \/>\n<h2><span id=\"Multiplying_Decimals\" class=\"m-toc-anchor\"><\/span>Multiplying Decimals<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Multiply \\(2.5 \\times 1.5\\)<\/div>\n<p>To multiply decimals, you first have to multiply the numbers as if they were whole numbers. Then, you can place the decimal point in the answer as needed.<\/p>\n<p>For \\(2.5 \\times 1.5\\), let&#8217;s first multiply the numbers with the decimal points removed.<\/p>\n<p style=\"text-align: center;\">\\(25\\times 15=375\\)<\/p>\n<p>Then, add up the total number of decimal places in the original numbers. Our original numbers, 2.5 and 1.5, each have one decimal place, so we have two decimal places total.<\/p>\n<p>This means we need to place the decimal point in our product (375) <strong>two<\/strong> places to the left.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-265882\" role=\"img\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/08\/375-decimal-move.svg\" alt=\"A decimal being moved two places to the left in the number 375\" width=\"177.8\" height=\"37.8\" \/><\/p>\n<p>Therefore, \\(2.5 \\times 1.5=3.75\\)!<\/p>\n<hr \/>\n<h2><span id=\"Dividing_Decimals\" class=\"m-toc-anchor\"><\/span>Dividing Decimals<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Divide \\(6.75 \\div 1.5\\)<\/div>\n<p>To divide decimals, you want to make the divisor a whole number.<\/p>\n<p>To do this for \\(6.75 \\div 1.5\\), let&#8217;s move the decimal point in the divisor to the right until it becomes a whole number. In this case, move it one place to get the whole number 15.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-265876\" role=\"img\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/08\/1.5-decimal-move.svg\" alt=\"A decimal being moved one place to the right in the number 1.5\" width=\"141.4\" height=\"37.8\" \/><\/p>\n<p>Then, move the decimal point in the dividend the same number of places to the right. In this case, 6.75 becomes 67.5.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-265879\" role=\"img\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/08\/6.75-decimal-move.svg\" alt=\"A decimal being moved one place to the right in the number 6.75\" width=\"155.4\" height=\"37.8\" \/><\/p>\n<p>Next, divide the new numbers as you normally would.<\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-265870\" role=\"img\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/08\/67.5-divided-by-15.svg\" alt=\"Long division problem for 67.5 divided by 15\" width=\"75.609625\" height=\"129.6165\" \/><\/p>\n<p>Therefore, \\(6.75 \\div 1.5=4.5\\)!<\/p>\n<hr \/>\n<h2><span id=\"Decimals_with_Exponents\" class=\"m-toc-anchor\"><\/span>Decimals with Exponents<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Calculate 2.5<sup>-2<\/sup><\/div>\n<p>Here, we have a negative exponent. This means you should find the reciprocal of the base raised to the positive exponent. So, 2.5<sup>-2<\/sup> is the same as \\(1 \\div 2.5^2\\).<\/p>\n<p>First, we need to calculate the exponent.<\/p>\n<p style=\"text-align: center;\">\\(2.5^2=2.5\\times 2.5\\)<\/p>\n<p>Then, remove the decimals and multiply.<\/p>\n<p style=\"text-align: center;\">\\(25 \\times 25=625\\)<\/p>\n<p>Next, add up the number of decimal places we had before removing them. We had two in this case, so place the decimal two places to the left to get 6.25.<\/p>\n<p>Now, we need to find the reciprocal, which is \\(1 \\div 6.25\\). To solve this, make the divisor and dividend whole numbers by moving the decimal two places to the right.<\/p>\n<p style=\"text-align: center;\">\\(100 \\div 625=0.16\\)<\/p>\n<p>Therefore, \\(2.5^{-2} =0.16\\)!<\/p>\n<hr \/>\n<h2><span id=\"Decimals_with_Roots\" class=\"m-toc-anchor\"><\/span>Decimals with Roots<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Find \\(\\sqrt[\\Large{3}]{0.125}\\)<\/div>\n<p>Our example is a cube root. This means we&#8217;re looking for a number that, when multiplied by itself three times, equals the number under the root symbol.<\/p>\n<p>In other words, we&#8217;re looking for a number \\(x\\) such that \\(x\\times x \\times x=0.125\\).<\/p>\n<p>To start, think about whole numbers. Ignore the decimal and consider the whole number 125. We know that \\(5 \\times 5\\times 5=125\\).<\/p>\n<p>With that in mind, our target of 0.125 has three decimal places. If we try \\(x= 0.5\\), then multiplying it three times will result in an answer with three decimal places.<\/p>\n<p style=\"text-align: center;\">\\(0.5 \\times 0.5 \\times 0.5=0.125\\)<\/p>\n<p>That shows us that \\(\\sqrt[\\Large{3}]{0.125}=0.5\\)!<\/p>\n<hr \/>\n<h2><span id=\"Decimals_with_Logarithms\" class=\"m-toc-anchor\"><\/span>Decimals with Logarithms<\/h2>\n<div style=\"border-left: solid 4px #ffcc00; border-top: solid 1px #ffcc00; border-bottom: solid 1px #ffcc00; border-right: solid 1px #ffcc00; border-radius: 0 5px 5px 0; padding: 10px; font-weight: 600; box-shadow: 1px 1px 2px grey; width: max-content; margin-bottom: 1.5em;\">\ud83d\udca1 Solve \\(\\log_{5}(0.04)\\)<\/div>\n<p>For this example, the logarithm asks: &#8220;What exponent do I need to put on the base (5) to get the number 0.04?&#8221;<\/p>\n<p>In other words, we&#8217;re trying to solve \\(5^?=0.04\\).<\/p>\n<p>To start, convert the decimal 0.04 to a fraction and simplify it.<\/p>\n<p style=\"text-align: center;\">\\(0.04 = \\dfrac{4}{100}=\\dfrac{1}{25}\\)<\/p>\n<p>So our equation \\(5^?=0.04\\) becomes \\(5^?=\\dfrac{1}{25}\\).<\/p>\n<p>Next, we need to express the fraction&#8217;s denominator using the base. We know that \\(5^2=25\\), so \\(\\dfrac{1}{25}\\) is the same is \\(\\dfrac{1}{5^2}\\).<\/p>\n<p>This is where the rule of negative exponents comes in. Remember that \\(\\dfrac{1}{x^n}=x^{-n}\\). So \\(\\dfrac{1}{5^2}\\) is the same as 5<sup>-2<\/sup>.<\/p>\n<p>Finally, we can solve for the exponent. Our equation is now \\(5^?=5^{-2}\\). Since the bases are the same, the exponents must be equal.<\/p>\n<p>That shows us that \\(\\log_{5}(0.04)=-2\\)!<\/p>\n<div class=\"home-buttons2\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/adding-and-subtracting-decimals\/\">Learn More About Decimals Here!<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Use this calculator to perform an operation on any two decimal numbers. Select from the dropdown menu to add, subtract, multiply, divide, or even more. a b + AddSubtractMultiplyDivideExponentRootLogarithm a+b=? Found a bug? Let us know! Adding Decimals \ud83d\udca1 Add To add decimals, you line up the decimal points and add the numbers as you &#8230; <a title=\"Decimal Calculator\" class=\"read-more\" href=\"https:\/\/www.mometrix.com\/academy\/decimal-calculator\/\" aria-label=\"Read more about Decimal Calculator\">Read more<\/a><\/p>\n","protected":false},"author":68,"featured_media":265927,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-213614","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_type-calculator"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213614","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/68"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=213614"}],"version-history":[{"count":9,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213614\/revisions"}],"predecessor-version":[{"id":291149,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/213614\/revisions\/291149"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/265927"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=213614"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}