4MA1/1H Nov 2021, Question 18: Recurring Decimals
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 3 marks
اقرأ هذا الحل مشروحاً بالعربي ←
The question, in short
Express the recurring decimal 0.4xxx…, where x is a whole number from 1 to 9, as a fraction in terms of x in simplest form, showing algebraic working.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Solution · 3 marks
- 1Let y = 0.4x̄, where the bar is over the x only
- 2Then y = 0.4xxxx...
- 3Multiply by 10: 10y = 4.xxxx...
- 4Multiply by 100: 100y = 4x.xxxx...
- 5Subtract 10y from 100y: 100y − 10y = 4x.xxxx... − 4.xxxx...
- 6So 90y = (4x − 4)
- 7Now 4x means 40 + x as a number, so 4x − 4 = 40 + x − 4 = 36 + x
- 8Therefore 90y = 36 + x
- 9So y = (36 + x)/90
Answer(36 + x)/90
Stuck on a step? Read the free lesson: Recurring Decimals
Practise more recurring decimals questions
Real 4MA1 past-paper questions, marked on your working like the exam, with a worked solution for every part.
Practise free on LemmaraMore past-paper questions on recurring decimals
Also searched as: 4MA1 1H November 2021 · 4MA1/1H · 4ma1 nov21 1h · question 18.
Lemmara is an independent study tool, not affiliated with or endorsed by Pearson Edexcel. The worked solutions are Lemmara’s own.