{"id":26150,"date":"2025-06-19T10:37:39","date_gmt":"2025-06-19T10:37:39","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=26150"},"modified":"2025-06-19T10:37:42","modified_gmt":"2025-06-19T10:37:42","slug":"what-expressions-are-equal-to-10-to-the-power-of-negative-5","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/what-expressions-are-equal-to-10-to-the-power-of-negative-5\/","title":{"rendered":"What expressions are equal to 10 to the power of negative 5"},"content":{"rendered":"\n<p>What expressions are equal to 10 to the power of negative 5<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>Expressions equal to 10\u2212510^{-5} include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>1105\\frac{1}{10^5}<\/li>\n\n\n\n<li>0.000010.00001<\/li>\n\n\n\n<li>1\u00d710\u221251 \\times 10^{-5}<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Explanation (Approx. 300 words)<\/strong><\/h3>\n\n\n\n<p>The expression 10\u2212510^{-5} is an example of a number written in <strong>scientific notation<\/strong> with a <strong>negative exponent<\/strong>. Understanding negative exponents is key to converting this into equivalent expressions.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Meaning of 10\u2212510^{-5}:<\/strong><\/h4>\n\n\n\n<p>The negative exponent tells us to take the <strong>reciprocal<\/strong> of the base raised to the positive exponent: 10\u22125=110510^{-5} = \\frac{1}{10^5}<\/p>\n\n\n\n<p>So instead of multiplying 10 by itself five times, you <strong>divide 1 by 10^5<\/strong>.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Step-by-step calculation:<\/strong><\/h4>\n\n\n\n<p>105=10\u00d710\u00d710\u00d710\u00d710=100,00010^5 = 10 \\times 10 \\times 10 \\times 10 \\times 10 = 100,000 10\u22125=1100,000=0.0000110^{-5} = \\frac{1}{100,000} = 0.00001<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Alternative Expressions:<\/strong><\/h4>\n\n\n\n<p>All of the following are mathematically equivalent to 10\u2212510^{-5}:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Fraction form<\/strong>:<br>1100,000\\frac{1}{100,000}<\/li>\n\n\n\n<li><strong>Decimal form<\/strong>:<br>0.000010.00001<\/li>\n\n\n\n<li><strong>Scientific notation<\/strong>:<br>1\u00d710\u221251 \\times 10^{-5}<\/li>\n<\/ol>\n\n\n\n<p>These forms are used in different contexts. Scientists often prefer <strong>scientific notation<\/strong> for very small or very large numbers because it&#8217;s more compact and readable.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Why it\u2019s Important:<\/strong><\/h4>\n\n\n\n<p>Understanding how to interpret and convert powers of 10, especially with negative exponents, is essential in math and science. It helps you work with measurements like micrometers (10\u2212610^{-6} meters), nanoseconds (10\u2212910^{-9} seconds), and very small concentrations in chemistry.<\/p>\n\n\n\n<p>So, when you see 10\u2212510^{-5}, you can confidently say it&#8217;s equal to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One hundred-thousandth<\/li>\n\n\n\n<li>0.00001<\/li>\n\n\n\n<li>1105\\frac{1}{10^5}<\/li>\n\n\n\n<li>1\u00d710\u221251 \\times 10^{-5}<\/li>\n<\/ul>\n\n\n\n<p>All are correct and interchangeable depending on the context.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>What expressions are equal to 10 to the power of negative 5 The correct answer and explanation is: Correct Answer:Expressions equal to 10\u2212510^{-5} include: Explanation (Approx. 300 words) The expression 10\u2212510^{-5} is an example of a number written in scientific notation with a negative exponent. Understanding negative exponents is key to converting this into equivalent [&hellip;]<\/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-26150","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26150","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=26150"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26150\/revisions"}],"predecessor-version":[{"id":26151,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/26150\/revisions\/26151"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=26150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=26150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=26150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}