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# Decimals

Coins are often used to express a fraction of a currency. In the US, a quarter is $0.25 and a dime is$0.10. Counting change is just one of many ways you can put decimals to use in everyday life.

# Decimals: Level 2 Challenges

If the following infinite series $$S$$ is evaluated as a decimal,what is the 37th digit to the right of the decimal place?

$\large S=\frac { 1 }{ 9 } +\frac { 1 }{ 99 } +\frac { 1 }{ 999 } +\ldots + \frac { 1 }{ { 10 }^{ n }-1 } + \ldots$

Which of the following is equal to

$0.123 \, 123 \, 123 \, 123 \, \ldots ?$

Without actual division find out which of the following rational numbers has a terminating decimal expansion

P)$$\frac { 17 }{ 90 }$$

Q)$$\frac { 33 }{ 50 }$$

R)$$\frac { 121 }{ { 2 }^{ 2 }\times { 5 }^{ 3 } }$$

S)$$\frac { 121 }{ { 2 }^{ 3 }\times { 3 }^{ 2 }\times { 7 }^{ 5 } }$$

True or False:

$1 > 0.99999\ldots$

$0.20\overline{16}=0.2016161616\ldots =\frac{a}{b}$

Given that $$a$$ and $$b$$ are coprime positive integers, find $$a+b$$.

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