{"id":46299,"date":"2025-07-02T02:59:50","date_gmt":"2025-07-02T02:59:50","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=46299"},"modified":"2025-07-02T02:59:52","modified_gmt":"2025-07-02T02:59:52","slug":"convert-by-using-unit-factors","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/convert-by-using-unit-factors\/","title":{"rendered":"Convert by using unit factors"},"content":{"rendered":"\n

Convert by using unit factors Show setups at right: (a) 17 m dm 11 \/ 0. | (b) 1.5 kg 8 (c) 14 cm (d) 1.7 pL (e) 9.25 m? cm? (0 3.4 km: m? 3, 4n<\/p>\n\n\n\n

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

Here are the correct answers for the unit conversions:<\/p>\n\n\n\n

(a) 17 m = 170<\/strong> dm
(b) 1.5 kg = 1500<\/strong> g
(c) 14 cm = 0.14<\/strong> m
(d) 1.7 \u00b5L = 0.0000017<\/strong> L
(e) 9.25 m\u00b2 = 92,500<\/strong> cm\u00b2
(f) 3.4 km\u00b3 = 3,400,000,000<\/strong> m\u00b3<\/p>\n\n\n\n

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

This problem requires converting measurements using unit factors<\/strong>, a method also known as dimensional analysis. This technique involves multiplying the original quantity by a conversion factor\u2014a fraction that equals one\u2014to change the units without altering the value. A unit factor is created from an equality, such as 1 meter = 10 decimeters. This can be written as the fraction (10 dm \/ 1 m) or (1 m \/ 10 dm), both of which are equal to one. You choose the fraction that allows the original unit to cancel out, leaving the desired unit.<\/p>\n\n\n\n

(a) 17 m to dm:<\/strong> Since 1 meter equals 10 decimeters, the unit factor needed is (10 dm \/ 1 m) to cancel out meters.
Setup: 17 m \u00d7 (10 dm \/ 1 m) = 170 dm<\/strong><\/p>\n\n\n\n

(b) 1.5 kg to g:<\/strong> The prefix “kilo” means 1000, so 1 kilogram equals 1000 grams.
Setup: 1.5 kg \u00d7 (1000 g \/ 1 kg) = 1500 g<\/strong><\/p>\n\n\n\n

(c) 14 cm to m:<\/strong> The prefix “centi” means 1\/100, so 100 centimeters are in 1 meter. To cancel centimeters, we place it in the denominator.
Setup: 14 cm \u00d7 (1 m \/ 100 cm) = 0.14 m<\/strong><\/p>\n\n\n\n

(d) 1.7 \u00b5L to L:<\/strong> The prefix “micro” (\u00b5) means one-millionth, so 1 liter contains 1,000,000 microliters.
Setup: 1.7 \u00b5L \u00d7 (1 L \/ 1,000,000 \u00b5L) = 0.0000017 L<\/strong> (or 1.7 x 10\u207b\u2076 L)<\/p>\n\n\n\n

(e) 9.25 m\u00b2 to cm\u00b2:<\/strong> For area conversions, the linear unit factor must be squared. Since 1 m = 100 cm, we square the entire relationship: (1 m)\u00b2 = (100 cm)\u00b2, which gives 1 m\u00b2 = 10,000 cm\u00b2.
Setup: 9.25 m\u00b2 \u00d7 (10,000 cm\u00b2 \/ 1 m\u00b2) = 92,500 cm\u00b2<\/strong><\/p>\n\n\n\n

(f) 3.4 km\u00b3 to m\u00b3:<\/strong> For volume, the linear unit factor is cubed. Since 1 km = 1000 m, we cube the relationship: (1 km)\u00b3 = (1000 m)\u00b3, which gives 1 km\u00b3 = 1,000,000,000 m\u00b3.
Setup: 3.4 km\u00b3 \u00d7 (1,000,000,000 m\u00b3 \/ 1 km\u00b3) = 3,400,000,000 m\u00b3<\/strong><\/p>\n\n\n\n

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

Convert by using unit factors Show setups at right: (a) 17 m dm 11 \/ 0. | (b) 1.5 kg 8 (c) 14 cm (d) 1.7 pL (e) 9.25 m? cm? (0 3.4 km: m? 3, 4n The Correct Answer and Explanation is: Here are the correct answers for the unit conversions: (a) 17 m […]<\/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-46299","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46299","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=46299"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46299\/revisions"}],"predecessor-version":[{"id":46302,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/46299\/revisions\/46302"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=46299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=46299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=46299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}