{"id":37826,"date":"2025-06-26T06:34:40","date_gmt":"2025-06-26T06:34:40","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=37826"},"modified":"2025-06-26T06:34:41","modified_gmt":"2025-06-26T06:34:41","slug":"what-is-the-value-of-0-6-0-3","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-is-the-value-of-0-6-0-3\/","title":{"rendered":"What is the value of 0.6 + 0.3"},"content":{"rendered":"\n

What is the value of 0.6 + 0.3? Write your answer as a fraction in lowest terms. 0.6 is repeated.<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the value of 0.6 (repeating) + 0.3<\/strong>, we will first convert both numbers into fractions, then add them.<\/p>\n\n\n\n

\n\n\n\n

Step 1: Convert 0.6 repeating<\/strong> to a fraction<\/h3>\n\n\n\n

Let:<\/p>\n\n\n\n

x = 0.666…<\/strong><\/p>\n\n\n\n

Multiply both sides by 10:<\/p>\n\n\n\n

10x = 6.666…<\/strong><\/p>\n\n\n\n

Now subtract the original equation:<\/p>\n\n\n\n

10x \u2212 x = 6.666… \u2212 0.666…<\/strong><\/p>\n\n\n\n

9x = 6<\/strong><\/p>\n\n\n\n

x = 6\/9<\/strong><\/p>\n\n\n\n

Simplify:<\/p>\n\n\n\n

x = 2\/3<\/strong><\/p>\n\n\n\n

So, 0.6 repeating = 2\/3<\/strong><\/p>\n\n\n\n

\n\n\n\n

Step 2: Convert 0.3<\/strong> to a fraction<\/h3>\n\n\n\n

0.3 = 3\/10<\/strong><\/p>\n\n\n\n

\n\n\n\n

Step 3: Add the two fractions<\/h3>\n\n\n\n

We are adding:<\/p>\n\n\n\n

2\/3 + 3\/10<\/strong><\/p>\n\n\n\n

To add these, find a common denominator. The least common denominator of 3 and 10 is 30.<\/p>\n\n\n\n

Convert both fractions:<\/p>\n\n\n\n

    \n
  • 2\/3=(2\u00d710)\/(3\u00d710)=20\/302\/3 = (2\u00d710)\/(3\u00d710) = 20\/302\/3=(2\u00d710)\/(3\u00d710)=20\/30<\/li>\n\n\n\n
  • 3\/10=(3\u00d73)\/(10\u00d73)=9\/303\/10 = (3\u00d73)\/(10\u00d73) = 9\/303\/10=(3\u00d73)\/(10\u00d73)=9\/30<\/li>\n<\/ul>\n\n\n\n

    Now add:<\/p>\n\n\n\n

    20\/30 + 9\/30 = 29\/30<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    0.6 (repeating) + 0.3 = 29\/30<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Explanation<\/h3>\n\n\n\n

    To solve the expression 0.6 repeating plus 0.3<\/strong>, we begin by understanding what each number represents. The number 0.6 repeating<\/strong>, written as 0.666…<\/strong>, means the digit 6 continues forever. This is a recurring decimal, and recurring decimals can be expressed exactly as fractions. The method to convert such decimals involves algebra.<\/p>\n\n\n\n

    We let x = 0.666…<\/strong> and multiply both sides by 10 to shift the decimal point. Doing this gives us 10x = 6.666…<\/strong>. Subtracting the original value x = 0.666…<\/strong> from this equation removes the repeating part, resulting in 9x = 6<\/strong>. Solving for x<\/strong> gives x = 6\/9<\/strong>, which simplifies to 2\/3<\/strong>.<\/p>\n\n\n\n

    Next, we convert 0.3<\/strong> into a fraction. Since 0.3<\/strong> is a terminating decimal, we can write it as 3\/10<\/strong>. Now we want to add 2\/3 + 3\/10<\/strong>. To do this, we find a common denominator. The least common denominator of 3 and 10 is 30. We convert both fractions so they have the same denominator: 2\/3 becomes 20\/30<\/strong>, and 3\/10 becomes 9\/30<\/strong>.<\/p>\n\n\n\n

    Adding them gives us 20\/30 + 9\/30 = 29\/30<\/strong>.<\/p>\n\n\n\n

    Therefore, 0.6 repeating plus 0.3 equals 29\/30<\/strong>, which is the correct answer in lowest terms.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    What is the value of 0.6 + 0.3? Write your answer as a fraction in lowest terms. 0.6 is repeated. The Correct Answer and Explanation is: To find the value of 0.6 (repeating) + 0.3, we will first convert both numbers into fractions, then add them. Step 1: Convert 0.6 repeating to a fraction Let: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-37826","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37826","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=37826"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37826\/revisions"}],"predecessor-version":[{"id":37831,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/37826\/revisions\/37831"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=37826"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=37826"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=37826"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}