1989 AMC 8 Problem 13

Question

Which of the following is equal to

\frac{9}{7 \times 53}?

\dfrac{0.9}{0.7 \times 53}

\dfrac{0.9}{0.7 \times 0.53}

\dfrac{0.9}{0.7 \times 5.3}

\dfrac{0.9}{7 \times 0.53}

\dfrac{0.09}{0.07 \times 0.53}

Dividing the numerator and one factor of the denominator by the same number keeps the fraction unchanged

To turn

9

into

0.9,

divide by

10;

to keep the value equal, divide one factor of the denominator by

10

as well

To rewrite the numerator

9

as

0.9,

divide it by

10.

To keep the fraction equal, divide the denominator by

10

too, which means dividing one of its factors by

10.

Dividing the factor

7

by

10

gives

\frac{0.9}{0.7 \times 53},

which equals the original. Each other choice changes the value by a factor of

10

or

100.

Thus, the correct answer is A .

Problem 13 in other years