OMG Can you tell me why my answer isn't ALSO right? Please?

Question

What is the area of a rectangle in square centimeters that is 4.00 inches by 5/6 inch?

Seems simple enough, right?

Well, I first multiplied (4)(5/6) and got 3.33 in. In order to get cm I did:

1 in/ 2.54 cm = 3.33 in / x cm.

I got x to be 8.45 cm and lo and behold that was an answer on the multiple choice so I picked it. Turns out I was wrong and the answer was (10.16 cm) * (2.17 cm) = 22.1 cm

I just converted it all at once in the end...WHY DONT WE GET THE SAME ANSWERS? What's the difference of converting the two sides from in. to cm. early on when you can just change it at the end. Ugh.....Help?

Answer 1

I'm just trying to really clear this up. But some friends have given the right point.

1st calculation (the right one)

((4 in)*(2.54 cm/in)) *((5/6 in)*(2.54 cm/in)) = 10.16 cm * 2.1167 cm = 21.5cm square


2nd calculation (yours)

(4 in) * (5/6 in) = 3.33 in square.
you then converdted it with
(3.33 in square) * (2.54 cm/in) = 8.45 in.cm
Pay attention to the unit. Your result is supposed to be in cm square.
In order to make it right, convert the resting in to cm

(8.34 in.cm) *(2.54 cm/in) = 21.18 cm square

(the final result might not be exactly same because i rounded the numbers up)

Answer 2

If you convert the measurments to cm at the start you will be able to work this out a lot easier.

You've probably made the mistake that a square inch can be converted into a square cm by converting it in the same way. It can't.

(I use 1 inch = 2.53cm for these conversions)

So 4 in = 10.16 cm

and 5/6 in = 2.11 cm

So the area = 10.16 x 2.11

= 21.44cm^2

Which is about what you got.

Answer 3

Because you used the linear conversion factor. There is another conversion factor from inch square to cm square.

1 inch length is 2.54 cm. This works in a straight line but you can not use it to convert areas.

This is the conversion factor. Each inch is 2.54cm right? So the area of each square inch is 2.54*2.54=6.45 cm squared

They chose that value to trick you and you fell for it. So you multiply 6.45 * 3.33 and you get 21.5 cm squared.

Where did 22.1cm come from? That is clearly wrong.

Answer 4

You are confusing linear measurements with area. Centimeters are linear and 2.54 cm = 1 inch. However, area uses square measurements and 2.54 cm^2 does not = 1 inch^2.
The area conversion is 6.45 cm^2 = 1 inch^2.

Answer 5

The numbers are right, but the units are wrong.

3.33 inches^2 is correct - you have square inches, not just inches.

To get cm^2, you have to convert by 1 in^2/ (2.54 cm)^2

You were missing one of your (1 in/(2.54 cm)) conversion factors, so your answer was off by that factor.

Answer 6

The mistake you made was multiplying the dimensions by each other first, which means you had square inches, but then you multiplied that by the LINEAR cm-to-inch conversion factor.

Convert the INDIVIDUAL measures to centimetres, and THEN multiply them together, and you will have the correct answer in square centimetres.

Note that when it's done correctly the conversion factor appears twice, but you only used it once; that made your answer too small by a factor of 2.54.

Answer 7

You converted wrong.

You did 4(5/6) and got 3.33 square inches, not just inches.

To convert from square inches to square cms, you can't just use 2.54. You would have wanted 2.54(2.54) = 6.45 cm squared

1 square inch/6.45 square cm = 3.33 square in/ x square cm

Answer 8

Area is in inches squared not in inches. So you have that 1 in^2 = (2.54)^2 cm^2. So you just need to change your last step.

Answer 9

S= 4*5/6 =10/3 inch^2
1 inch= 2.54 cm so 1inch^2 = (2.54)^2 cm^2 =6.45 cm^2
So you area incm^2 is 21.5 cm^2
There may be rounding errors by supressing decimals

Answer 10

You cannot convert cm^2 to inches^2 just by using the formula to convert cm to inches or vice versa. You have to convert before you calculate the area.