# Converting decimal to fraction problem (algebra included)

#### RebelSchool

So my math book gave me a proportion problem involving two triangles. It basically came down to this.

AC/DE = AB/DB

AC = 12 inches, AB = 22 inches, and DB = 14 inches,

So we have to solve for DE.

ok.

12/DE = 22/14

22(DE) = 168

168 ÷ 22 = 7.64

7.64 = 7 and 16/25

I am wrong.

the book says it is 7 and 7/11

i am confuzzled and need help as to how they are getting that 7/11.

#### math951

AC/DE=AB/DB

(DE)(AB)=(AC)(DB)
(DE)(22)=(12)(14)
(DE)(22)=168 -- divide 22 by both sides.
168/22 simplifies to 84/11
DE= 84/11, which is equal to 7 and 7/11 as mixed fraction correct? 11*7+7=84/11

#### Archie

168 ÷ 22 = 7.64

7.64 = 7 and 16/25
$168 \div 22 \ne 7.64$ but $168 \div 22 = \frac{84}{11} = 7.\dot6 \dot3 = 7.6363636363 \ldots$

By converting into decimals, you have made an approximation (rounding to the nearest $\frac1{100}$) and thus introduced an error.

In general, you should avoid decimals entirely unless you are asked for an answer in decimals, when you should only convert the final answer. This is because the error introduced by rounding a decimal can grow considerably under later operations.

If you really have to use decimals earlier, you should always use many more decimal places than you are going to need in the final answer.