Fractions, Decimals, and Percents - ISEE Middle Level Quantitative Reasoning

1. What is $3.5\%$ as a decimal?

   $0.035$. Dividing $3.5$ by $100$ moves the decimal two places left to get $0.035$.

2. What is $\frac{9}{20}$ as a percent?

   $45\%$. Multiplying $\frac{9}{20}$ by $100$ gives $45$ after division.

3. What is $45\%$ as a decimal?

   $0.45$. Dividing $45$ by $100$ moves the decimal two places left to get $0.45$.

4. What is $\frac{1}{4}$ as a decimal?

   $0.25$. Dividing $1$ by $4$ yields $0.25$ as the decimal form.

5. What is $\frac{1}{2}$ as a decimal?

   $0.5$. Dividing $1$ by $2$ yields $0.5$ as the decimal form.

6. What is the rule for converting a fraction $\frac{a}{b}$ to a percent?

   Compute $\frac{a}{b}\times 100\%$. Multiplying the decimal equivalent of the fraction by $100$ gives the percentage value.

7. What is $37.5\%$ as a fraction in simplest form?

   $\frac{3}{8}$. Converting $37.5\%$ to $\frac{37.5}{100}$ equals $\frac{375}{1000}$, simplified by dividing by $125$ to get $\frac{3}{8}$.

8. What is the rule for converting a fraction $\frac{a}{b}$ to a decimal?

   Compute $a\div b$. Dividing the numerator by the denominator yields the decimal representation of the fraction.

9. What is $\frac{3}{4}$ as a decimal?

   $0.75$. Dividing $3$ by $4$ yields $0.75$ as the decimal form.

10. What is $\frac{11}{25}$ as a percent?

    $44\%$. Multiplying $\frac{11}{25}$ by $100$ gives $44$ after division.

11. What is $0.03$ as a fraction in simplest form?

    $\frac{3}{100}$. Expressing $0.03$ as $\frac{3}{100}$, which is already in simplest form since $3$ and $100$ share no common factors other than $1$.

12. What is $0.75$ as a percent?

    $75\%$. Multiplying $0.75$ by $100$ shifts the decimal two places right to get $75$.

13. What is the rule for converting a percent $p\%$ to a fraction in simplest form?

    Write $\frac{p}{100}$, then simplify. Expressing the percent as a fraction over $100$ and reducing it provides the simplest fractional form.

14. What is $\frac{2}{3}$ as a percent, rounded to the nearest whole percent?

    $67\%$. Dividing $2$ by $3$ gives approximately $0.6667$, multiplied by $100$ is about $66.67$, which rounds to $67$.

15. What is $\frac{7}{10}$ as a percent?

    $70\%$. Multiplying $\frac{7}{10}$ by $100$ gives $70$ after division.

16. What is $0.6$ as a fraction in simplest form?

    $\frac{3}{5}$. Expressing $0.6$ as $\frac{6}{10}$ and simplifying by dividing numerator and denominator by $2$ yields $\frac{3}{5}$.

17. What is $0.125$ as a fraction in simplest form?

    $\frac{1}{8}$. Expressing $0.125$ as $\frac{125}{1000}$ and simplifying by dividing numerator and denominator by $125$ yields $\frac{1}{8}$.

18. What is $\frac{1}{5}$ as a decimal?

    $0.2$. Dividing $1$ by $5$ yields $0.2$ as the decimal form.

19. What is $\frac{1}{8}$ as a decimal?

    $0.125$. Dividing $1$ by $8$ yields $0.125$ as the decimal form.

20. What is the rule for converting a decimal $d$ to a percent?

    Multiply by $100$ and add $\%$: $d\to 100d\%$. Multiplying the decimal by $100$ shifts the decimal point two places to the right to express it as a percentage of $100$.

21. What is the rule for converting a percent $p\%$ to a decimal?

    Divide by $100$: $p\%\to \frac{p}{100}$. Dividing the percent by $100$ moves the decimal point two places to the left to convert it to its decimal equivalent.

22. What is $125\%$ as a decimal?

    $1.25$. Dividing $125$ by $100$ moves the decimal two places left to get $1.25$.

23. What is $\frac{3}{5}$ as a percent?

    $60\%$. Multiplying $\frac{3}{5}$ by $100$ gives $60$ after division.

24. What is $0.08$ as a percent?

    $8\%$. Multiplying $0.08$ by $100$ shifts the decimal two places right to get $8$.

25. What is $1.2$ as a percent?

    $120\%$. Multiplying $1.2$ by $100$ shifts the decimal two places right to get $120$.

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