Algebraically Proving Recurring Decimals

23 Jun, 2021

The Corbettmaths Practice Questions on Recurring Decimals. Visit httpwww3minutemathscouk for quick reminder High School GCSE mathematics videos.

Total 1 Average 5 5 Indirect Proof Proof By Contradiction When Trying To Prove A Statement Is True It May Be Benefi Contradiction Basic Algebra Teaching

X 0dot1 4 dot7.

Algebraically proving recurring decimals. DT WRITE IN THIS AREA. Number 111 Recurring Decimals. Multiply both sides by textcolorblue10 for each decimal place that isnt recurring If there are none it stays as Step 1.

16 Use algebra to show that the recurring decimal 02813 557 1980 DO NOT WRITE IN THIS AREA Total for Question 16 is 2 marks 17 Using algebra prove that given any 3 consecutive even numbers the difference between the square of the largest number and the square of the smallest number is always 8 times the middle number. Change the following recurring decimals into fractions. Dot 3 means 0333333.

As with most mathematics aim for a logical progression with the equals sign in. The answer is to use algebra to show a formal proof. For example 0.

A repeating decimals to fractions question is a little more abstract but once you understand the principles it should be relatively straightforward. Let the number of recurring digits n. A short tutorialexample of how to prove stuff algebraically.

Some numbers cannot be expressed exactly as decimals with a finite number of digits. It can be shown that a number is rational if its decimal representation is repeating or terminating. Converting a recurring decimal to a fraction can be a stand alone exam question so it is certainly a skill you want to master.

11 Prove algebraically that the recurring decimal 0216 can be written as Total for question 11 is 2 marks 8 37. Write 0dot1 4 dot7 as a fraction in its simplest from. Home Edexcel GCSE Maths Topic Questions 1.

Prove algebraically that the recurring decimal 025 has the value 23 90 2 4. 12 Prove algebraically that the recurring decimal. - the decimal never ends.

And 0dot 2dot 7 is equal to. Dot notation is used with recurring decimals. Let x recurring decimal in expanded form.

Videos worksheets 5-a-day and much more. So it is a rational number named after ratio. This is typical of proof by algebra questions asked on GCSE papersThis tutorial was requested.

Subtract 1 from 3 to eliminate the recurring part. The dot above the number shows which numbers recur for example 05dot 7 is equal to 05777777. For example since 23 0666666666 to express the fraction 23 in the decimal system we require an infinity of 6s.

Such decimals are referred to as recurring or repeating decimals. The recurring decimal 07 3 can be written as a ratio of two integers having 11 as the numerator and 15 as the denominator. Multiply recurring decimal by 10 n.

Visit httpwwwmathswrapcouk for more videos hints and tips SATS to GCSEI hope the video helps and please do leave a comment - thanksVisit httpwww. A Write 5 11 as a recurring decimal. Solve for x expressing your answer as a fraction in its simplest form.

Recurring decimal to fraction. Make your number equal to x. X 0045 45 recurring.

Using algebra to prove that a recurring decimal equals a given fraction. Prove algebraically that x can be written as 122 x0045 45 recurring 10x 045 45 recurring. Circle the decimal that is closest in value to 2 3 1 06 066 0667 067 5.

Dot notation is used with recurring decimals. A recurring decimal exists when decimal numbers repeat forever. This video is all about how to convert a recurring decimal to a.

10 11 12 15 Prove algebraically that the recurring decimal 0681 can be written as 22 681 681 675 770 Total for question 10 is 2 marks Prove algebraically that the recumng decimal 0216 can be written as 37 26 p 6 26 000 37 Total for question 11 is 2 marks Prove algebraically that the recurring decimal 0126 can be written as 111 9 q q DC 26 Total for question 12 is 2 marks. Using algebra to prove that a recurring decimal equals a given fraction. 10 Prove algebraically that the recurring decimal 0681 can be written as Total for question 10 is 2 marks 15 22.

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