# Fractions and Decimals

Fractions and decimals appear everywhere in construction and design-related problems. Whenever one quantity is broken down into a number of smaller quantities (e.g. a wall width divided into three equally-long sub-widths), the resulting smaller quantities represent fractions of the original. Fractions can be whole numbers, but in practice they are usually numbers that lie between' whole numbers -- such as $1.75$, for example, which lies three quarters of the way between $1$ and $2$. Measurements that cannot be expressed as whole numbers are conventionally written in decimal notation.

$$\newcommand{\ctext}{\style{font-family:Arial}{\text{#1}}}$$

### Example problem The above image shows the floorplan of a single-story, four-bedroom house. The house has two identically-dimensioned main bedrooms with ensuites. For purposes of discussion, consider the Northernmost main bedroom / ensuite combination. This bedroom has floorspace dimensions $3000\;\ctext{mm} \times 3400\;\ctext{mm} = 10.2\;\ctext{m}^2$; its ensuite has dimensions $1500\;\ctext{mm} \times 3100\;\ctext{mm} = 4.65\;\ctext{m}^2$. Is the ensuite floor area more or less than half that of the bedroom? (Are there any rules of thumb' in this regard?)

### Solution

Written as a fraction, the ensuite floor area divided by the bedroom floor area is given by

$$\frac{\ctext{ensuite floor area}}{\ctext{bedroom floor area}}=\frac{4.65\;\ctext{m}^2}{0.20\;\ctext{m}^2}=4.65\;\ctext{m}^2\div 10.20\;\ctext{m}^2\approx 0.46$$

The rule of thumb is a half ($\frac{1}{2}$ or $0.5$).
{"ft_lang_label":"__label__en","ft_lang_prob":0.819959,"math_prob":0.99805546,"size":1425,"snap":"2022-27-2022-33","text_gpt3_token_len":379,"char_repetition_ratio":0.111189306,"word_repetition_ratio":0.0,"special_character_ratio":0.26666668,"punctuation_ratio":0.10569106,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.99338925,"pos_list":[0,1,2],"im_url_duplicate_count":[null,2,null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-06-27T01:48:09Z\",\"WARC-Record-ID\":\"<urn:uuid:3cf6d178-03cc-48a4-b83b-a46c0ff56ae8>\",\"Content-Length\":\"86346\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:d300586d-2257-48c8-8650-30a0277ca050>\",\"WARC-Concurrent-To\":\"<urn:uuid:7234b4c7-f314-4134-b332-906660889bec>\",\"WARC-IP-Address\":\"203.82.26.7\",\"WARC-Target-URI\":\"https://www.westernsydney.edu.au/mesh/mesh/disciplines_using_maths/construction_management/about_mathematics_used_in_construction/fractions_and_decimals\",\"WARC-Payload-Digest\":\"sha1:LOIR5O33JYPTYZS5Z6KZZIOPJ6HS6HCE\",\"WARC-Block-Digest\":\"sha1:ZBKZMB6LE7QZELLET3NPUJZL4PI7EWX7\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-27/CC-MAIN-2022-27_segments_1656103324665.17_warc_CC-MAIN-20220627012807-20220627042807-00454.warc.gz\"}"}