Form 3 Mathematics Questions

Kosa kamili ni tofauti kamili kati ya thamani iliyokadiriwa na thamani halisi.

$$\text{Kosa kamili} = \left|0.47 - \frac{4}{9}\right|$$

Ili kurahisisha hesabu, tunabadilisha 0.47 kuwa sehemu: $0.47 = \frac{47}{100}$.

$$\text{Kosa kamili} = \left|\frac{47}{100} - \frac{4}{9}\right|$$

Pata kigawo cha kawaida cha 100 na 9, ambacho ni 900.

$$\text{Kosa kamili} = \left|\frac{47 \times 9}{100 \times 9} - \frac{4 \times 100}{9 \times 100}\right|$$ $$\text{Kosa kamili} = \left|\frac{423}{900} - \frac{400}{900}\right|$$ $$\text{Kosa kamili} = \left|\frac{23}{900}\right| = \frac{23}{900}$$

Asilimia ya kosa = $\frac{\text{Kosa kamili}}{\text{Thamani halisi}} \times 100\%$

$$\text{Asilimia ya kosa} = \frac{\frac{23}{900}}{\frac{4}{9}} \times 100\%$$

Ili kurahisisha, tunazidisha na kinyume cha sehemu ya chini:

$$\text{Asilimia ya kosa} = \frac{23}{900} \times \frac{9}{4} \times 100\%$$ $$\text{Asilimia ya kosa} = \frac{23 \times 9}{900 \times 4} \times 100\%$$

Gawanya 900 kwa 9:

$$\text{Asilimia ya kosa} = \frac{23 \times 1}{100 \times 4} \times 100\%$$ $$\text{Asilimia ya kosa} = \frac{23}{400} \times 100\%$$ $$\text{Asilimia ya kosa} = \frac{23}{4}\%$$ $$\text{Asilimia ya kosa} = 5.75\%$$

Asilimia ya kosa ni $\boxed{5.75\%}$.