Question

write each decimal as a fraction or mixed number in simplest form.

1. 0.26
2. 0.75
3. 0.4
4. 0.1
5. 4.48
6. 9.8
7. 0.91
8. 11.15
9. 4.3

Explanation:

Step1: Convert 0.26 to fraction

0.26 has two decimal places, so we can write it as $\frac{26}{100}$. Then simplify by dividing numerator and denominator by their greatest common divisor, which is 2. So $\frac{26\div2}{100\div2}=\frac{13}{50}$.

Step2: Convert 0.75 to fraction

0.75 has two decimal places, so it is $\frac{75}{100}$. The GCD of 75 and 100 is 25. Dividing both by 25 gives $\frac{75\div25}{100\div25}=\frac{3}{4}$.

Step3: Convert 0.4 to fraction

0.4 has one decimal place, so it is $\frac{4}{10}$. Simplify by dividing numerator and denominator by 2: $\frac{4\div2}{10\div2}=\frac{2}{5}$.

Step4: Convert 0.1 to fraction

0.1 has one decimal place, so it is $\frac{1}{10}$.

Step5: Convert 4.48 to mixed number and fraction

The whole number part is 4. The decimal part 0.48 has two decimal places, so $\frac{48}{100}$. Simplify by dividing by 4: $\frac{48\div4}{100\div4}=\frac{12}{25}$. So 4.48 is $4\frac{12}{25}$ or $\frac{4\times25 + 12}{25}=\frac{112}{25}$.

Step6: Convert 9.8 to mixed number and fraction

Whole number part is 9. Decimal part 0.8 is $\frac{8}{10}=\frac{4}{5}$. So 9.8 is $9\frac{4}{5}$ or $\frac{9\times5 + 4}{5}=\frac{49}{5}$.

Step7: Convert 0.91 to fraction

0.91 has two decimal places, so $\frac{91}{100}$ (91 and 100 have no common divisor other than 1, so it's already in simplest form).

Step8: Convert 11.15 to mixed number and fraction

Whole number part 11. Decimal part 0.15 is $\frac{15}{100}=\frac{3}{20}$. So 11.15 is $11\frac{3}{20}$ or $\frac{11\times20 + 3}{20}=\frac{223}{20}$.

Step9: Convert 4.3 to mixed number and fraction

Whole number part 4. Decimal part 0.3 is $\frac{3}{10}$. So 4.3 is $4\frac{3}{10}$ or $\frac{4\times10 + 3}{10}=\frac{43}{10}$.

Answer:

1. $\frac{13}{50}$
2. $\frac{3}{4}$
3. $\frac{2}{5}$
4. $\frac{1}{10}$
5. $4\frac{12}{25}$ (or $\frac{112}{25}$)
6. $9\frac{4}{5}$ (or $\frac{49}{5}$)
7. $\frac{91}{100}$
8. $11\frac{3}{20}$ (or $\frac{223}{20}$)
9. $4\frac{3}{10}$ (or $\frac{43}{10}$)