## Percentages Formulas

1. Per cent is Per 100. Cent is 100.

The symbol for percent is %.

The fraction 1/100 is written for %

So, 50% is 50 × 1/100 = 50/100 = ½

2. Formulas on Percent Change:

1. Percent Increase is

(amount of increase/initial number) × 100%

2. Percent Decrease is

(amount of decrease/initial number) × 100%

3. Formulas on Percent Comparison:

1. Percent Greater (more) is

(difference of the numbers)/(smaller number) × 100%

2. Percent Smaller (less) is

(difference of the numbers)/(greater number) × 100%

4. Formulas on Percent (total) change during successive percent changes:

Note: In the following, + sign denotes increase, and – sign, decrease.

1. If a number N is increased first by x% and next by y%, then the total percent

change is

(x + y + (x y/100))%

2. If a number N is decreased first by x% and increased next by y%, then the total percent

change is

(- x + y - x y/100)%

3. If a number N is increased first by x% and decreased next by y%, then the total percent

change is

(+x – y –xy/100)%

5. Formulas on Three important concepts on percents:

1. Consider a number N.

It is successively increased twice by x% each time.

Then, the total percent increase is > 2x%

2. Consider a Number N.

It is successively decreased twice by x% each time.

Then, the total percent decrease is < 2x%

3. Consider a Number N.

It is successively increased and decreased by x% each time.

Then, the final value is less than the original value.
{"ft_lang_label":"__label__en","ft_lang_prob":0.8875236,"math_prob":0.999151,"size":1421,"snap":"2021-43-2021-49","text_gpt3_token_len":397,"char_repetition_ratio":0.17219478,"word_repetition_ratio":0.1923077,"special_character_ratio":0.31104857,"punctuation_ratio":0.13851352,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9993449,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-10-19T01:48:31Z\",\"WARC-Record-ID\":\"<urn:uuid:2507c942-af03-433d-bad7-af99401f3902>\",\"Content-Length\":\"29877\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:ff6ead41-df2f-4c84-8e5c-cca12a60e6f1>\",\"WARC-Concurrent-To\":\"<urn:uuid:d1ea9025-9fe5-44ee-84c4-97448089374f>\",\"WARC-IP-Address\":\"104.21.77.198\",\"WARC-Target-URI\":\"https://www.math-for-all-grades.com/PercentagesFormulas.html\",\"WARC-Payload-Digest\":\"sha1:KVKA2UHOANAS7UMDWES2YUZO426TA4HN\",\"WARC-Block-Digest\":\"sha1:MGA3WV3X2AGP7RAYYMGNBQH646RM6JGO\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-43/CC-MAIN-2021-43_segments_1634323585231.62_warc_CC-MAIN-20211019012407-20211019042407-00437.warc.gz\"}"}