Question

Choose the mixed numeral that is equivalent to this decimal 3.242424...

Answer 1

Answer:

First, we can write:

x

=

3

.

¯¯¯¯

24

Next, we can multiply each side by  

100

giving:

100

x

=

324

.

¯¯¯¯

24

Then we can subtract each side of the first equation from each side of the second equation giving:

100

x

−

x

=

324

.

¯¯¯¯

24

−

3

.

¯¯¯¯

24

We can now solve for  

x

as follows:

100

x

−

1

x

=

(

324

+

0

.

¯¯¯¯

24

)

−

(

3

+

0

.

¯¯¯¯

24

)

(

100

−

1

)

x

=

324

+

0

.

¯¯¯¯

24

−

3

−

0

.

¯¯¯¯

24

99

x

=

(

324

−

3

)

+

(

0

.

¯¯¯¯

24

−

0

.

¯¯¯¯

24

)

99

x

=

321

+

0

99

x

=

321

99

x

99

=

321

99

99

x

99

=

3

×

107

3

×

33

x

=

3

×

107

3

×

33

x

=

107

33

Now, we can convert this improper fraction to a mixed number:

x

=

107

33

=

99

+

8

33

=

99

33

+

8

33

=

3

+

8

33

=

3

8

33

3

.

¯¯¯¯

24

=

3

8

33