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1997 CEMC Pascal Problems/Problem 3

Problem

The value of $2\frac{1}{10} + 3\frac{11}{100} + 4\frac{111}{1000}$ is

$\text{ (A) }\ 9.321 \qquad\text{ (B) }\ 9.111 \qquad\text{ (C) }\ 9.123 \qquad\text{ (D) }\ 9.111111 \qquad\text{ (E) }\ 9.11081081$

Solution 1

We can convert the mixed numbers into decimal form, and then add the decimals together:

$2\frac{1}{10} + 3\frac{11}{100} + 4\frac{111}{1000} = 2.1 + 3.11 + 4.111 = 5.21 + 4.111 = \boxed {\textbf {(A) } 9.321}$

~anabel.disher

Solution 2

We can use a common denominator to add the fractions together, and then convert the resulting mixed number into a decimal:

$2\frac{1}{10} + 3\frac{11}{100} + 4\frac{111}{1000} = 2\frac{1 \times 100}{10 \times 100} + 3\frac{11 \times 10}{100 \times 10} + 4\frac{111 \times 1}{1000 \times 1}$ $= 2\frac{100}{1000} + 3\frac{110}{1000} + 4\frac{111}{1000} = 5\frac{210}{1000} + 4\frac{111}{1000} = 9\frac{321}{1000} = \boxed {\textbf {(A) } 9.321}$

~anabel.disher

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