To express the repeating decimal 1.29456456456\u20261.29456456456\\ldots1.29456456456\u2026 as a fraction, we can follow these steps:<\/p>\n\n\n\n
Step 1: Define the repeating decimal as a variable.<\/h3>\n\n\n\n
Let x=1.29456456456\u2026x = 1.29456456456\\ldotsx=1.29456456456\u2026, where the “45” repeats.<\/p>\n\n\n\n
Step 2: Eliminate the repeating part.<\/h3>\n\n\n\n
Since the repeating part is two digits long (“45”), we multiply both sides of the equation by 100 to shift the decimal point two places to the right:100x=129.456456456\u2026100x = 129.456456456\\ldots100x=129.456456456\u2026<\/p>\n\n\n\n
Step 3: Subtract the original equation from this new equation.<\/h3>\n\n\n\n
Now subtract the original equation x=1.29456456456\u2026x = 1.29456456456\\ldotsx=1.29456456456\u2026 from 100x=129.456456456\u2026100x = 129.456456456\\ldots100x=129.456456456\u2026:100x\u2212x=129.456456456\u2026\u22121.29456456456\u2026100x – x = 129.456456456\\ldots – 1.29456456456\\ldots100x\u2212x=129.456456456\u2026\u22121.29456456456\u2026<\/p>\n\n\n\n
Simplifying both sides:99x=128.161892892\u202699x = 128.161892892\\ldots99x=128.161892892\u2026<\/p>\n\n\n\n
Step 4: Separate the integer part and the decimal part.<\/h3>\n\n\n\n
Now separate the integer part from the decimal. The equation becomes:99x=128+0.161892892\u202699x = 128 + 0.161892892\\ldots99x=128+0.161892892\u2026<\/p>\n\n\n\n
Let\u2019s focus on the repeating decimal part. To handle this, we can now express the repeating part as a fraction.<\/p>\n\n\n\n
Step 5: Express the repeating decimal as a fraction.<\/h3>\n\n\n\n
Let y=0.161892892\u2026y = 0.161892892\\ldotsy=0.161892892\u2026. To convert yyy into a fraction, follow similar steps as we did for the original decimal.<\/p>\n\n\n\n
Multiply yyy by 1000 to shift the decimal three places:1000y=161.892892892\u20261000y = 161.892892892\\ldots1000y=161.892892892\u2026<\/p>\n\n\n\n
Subtract the original equation y=0.161892892\u2026y = 0.161892892\\ldotsy=0.161892892\u2026 from this new equation:1000y\u2212y=161.892892892\u2026\u22120.161892892\u20261000y – y = 161.892892892\\ldots – 0.161892892\\ldots1000y\u2212y=161.892892892\u2026\u22120.161892892\u2026<\/p>\n\n\n\n
Simplifying:999y=161.731999y = 161.731999y=161.731<\/p>\n\n\n\n
Now, solve for yyy:y=161.731999y = \\frac{161.731}{999}y=999161.731\u200b<\/p>\n\n\n\n
Step 6: Substitute back into the original equation.<\/h3>\n\n\n\n
Now we substitute the value of yyy into our equation for xxx:99x=128+161.73199999x = 128 + \\frac{161.731}{999}99x=128+999161.731\u200b<\/p>\n\n\n\n
Now, solve for xxx by dividing both sides by 99:x=128+161.73199999x = \\frac{128 + \\frac{161.731}{999}}{99}x=99128+999161.731\u200b\u200b<\/p>\n\n\n\n
After simplifying, we get:x=127389900x = \\frac{12738}{9900}x=990012738\u200b<\/p>\n\n\n\n
This fraction simplifies to the ratio of two integers.<\/p>\n\n\n\n
Final Answer:<\/h3>\n\n\n\n
The repeating decimal 1.29456456456\u20261.29456456456\\ldots1.29456456456\u2026 can be expressed as the fraction 127389900\\frac{12738}{9900}990012738\u200b.<\/p>\n\n\n\n Express the repeating decimal as the ratio of two integers. 1.29456 = 1.29456456456. The ratio of two integers is (Type an integer or a fraction The Correct Answer and Explanation is: To express the repeating decimal 1.29456456456\u20261.29456456456\\ldots1.29456456456\u2026 as a fraction, we can follow these steps: Step 1: Define the repeating decimal as a variable. 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-45348","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45348","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=45348"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45348\/revisions"}],"predecessor-version":[{"id":45350,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/45348\/revisions\/45350"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=45348"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=45348"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=45348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner5-15.jpeg\")
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