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Weekly Problem 49 - 2007

What is the mean of 1.2 recurring and 2.1 recurring?

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Spiralling Decimals

Take turns to place a decimal number on the spiral. Can you get three consecutive numbers?

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Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How are the following recurring decimals related?

$0.22222222$ .....
$2.22222222$ ......
$22.22222222$ ......
$222.22222222$ ......

How are these recurring decimals related?

$0.2525252525$ ......
$2.5252525252$ ......
$25.252525252$ ......
$252.52525252525$ ......

Which pairs can be related by a sum and which pairs can be related by a multiplication?

The numbers $2.2222222$ ... and $2.525252525252$ ... can be written as a fractions. What are they?