Question

write the percent as a decimal or the decimal as a percent. use a model to represent the numbers.

1. 81%
2. 0.91
3. 5%
4. 8%
5. 0.3%
6. 78%
7. 0.167
8. 0.293
9. 3.82
10. 210%
11. 100.8%
12. 0.125

write the fraction as a decimal and a percent.

1. \\(\frac{1}{4}\\)
2. \\(\frac{4}{3}\\)
3. \\(\frac{3}{5}\\)
4. \\(\frac{7}{10}\\)
5. \\(\frac{1}{150}\\)
6. \\(\frac{7}{25}\\)
7. \\(\frac{2}{11}\\)
8. \\(\frac{14}{5}\\)
9. \\(\frac{5}{9}\\)
10. \\(\frac{13}{20}\\)
11. \\(\frac{2}{25}\\)
12. \\(\frac{10}{3}\\)
13. your friend writes 1.475% as a decimal. is your friend correct? explain your reasoning.

\\(1.475\\% = 1.475\\% = 147.5\\%\\)

1. fifty - four percent of the students in your class have moved at least one time. write this percent as a decimal.
2. only 0.15 of the total number of vehicles in your school parking lot are buses. what percent of the vehicles are buses?
3. you spent 0.88 of your allowance this week. what percent of your allowance did you spend?
4. on a history test, you get \\(\frac{43}{50}\\) of the possible points. write a decimal and a percent that represent your score.
5. of the fluid that you drink on a typical day, \\(\frac{1}{10}\\) is milk and 50% is water. how many times more water do you drink than milk?

Explanation:

Step1: Convert % to decimal (divide by 100)

1. $81\% = \frac{81}{100} = 0.81$
2. $0.91 = 0.91 \times 100\% = 91\%$
3. $5\% = \frac{5}{100} = 0.05$
4. $8\% = \frac{8}{100} = 0.08$
5. $0.3\% = \frac{0.3}{100} = 0.003$
6. $78\% = \frac{78}{100} = 0.78$
7. $0.167 = 0.167 \times 100\% = 16.7\%$
8. $0.293 = 0.293 \times 100\% = 29.3\%$
9. $3.82 = 3.82 \times 100\% = 382\%$
10. $210\% = \frac{210}{100} = 2.1$
11. $100.8\% = \frac{100.8}{100} = 1.008$
12. $0.125 = 0.125 \times 100\% = 12.5\%$

Step2: Fraction to decimal/percent

1. $\frac{1}{4} = 0.25 = 0.25 \times 100\% = 25\%$
2. $\frac{4}{3} \approx 1.333 = 1.333 \times 100\% \approx 133.3\%$
3. $\frac{3}{5} = 0.6 = 0.6 \times 100\% = 60\%$
4. $\frac{7}{10} = 0.7 = 0.7 \times 100\% = 70\%$
5. $\frac{1}{150} \approx 0.0067 = 0.0067 \times 100\% \approx 0.67\%$
6. $\frac{7}{25} = 0.28 = 0.28 \times 100\% = 28\%$
7. $\frac{2}{11} \approx 0.1818 = 0.1818 \times 100\% \approx 18.18\%$
8. $\frac{14}{5} = 2.8 = 2.8 \times 100\% = 280\%$
9. $\frac{5}{9} \approx 0.5556 = 0.5556 \times 100\% \approx 55.56\%$
10. $\frac{13}{20} = 0.65 = 0.65 \times 100\% = 65\%$
11. $\frac{2}{25} = 0.08 = 0.08 \times 100\% = 8\%$
12. $\frac{10}{3} \approx 3.333 = 3.333 \times 100\% \approx 333.3\%$

Step3: Check friend's calculation

1. Convert $1.475\%$ to decimal: $\frac{1.475}{100} = 0.01475$. Friend incorrectly multiplied by 100 instead of dividing, so they are wrong.

Step4: Percent to decimal

1. $54\% = \frac{54}{100} = 0.54$

Step5: Decimal to percent

1. $0.15 = 0.15 \times 100\% = 15\%$

Step6: Decimal to percent

1. $0.88 = 0.88 \times 100\% = 88\%$

Step7: Fraction to decimal/percent

1. $\frac{43}{50} = 0.86 = 0.86 \times 100\% = 86\%$

Step8: Compare water to milk

1. Convert $\frac{1}{10}$ to percent: $\frac{1}{10}=0.1=10\%$. Divide water percent by milk percent: $\frac{50\%}{10\%}=5$

Answer:

1. $0.81$
2. $91\%$
3. $0.05$
4. $0.08$
5. $0.003$
6. $0.78$
7. $16.7\%$
8. $29.3\%$
9. $382\%$
10. $2.1$
11. $1.008$
12. $12.5\%$
13. Decimal: $0.25$, Percent: $25\%$
14. Decimal: $\approx1.333$, Percent: $\approx133.3\%$
15. Decimal: $0.6$, Percent: $60\%$
16. Decimal: $0.7$, Percent: $70\%$
17. Decimal: $\approx0.0067$, Percent: $\approx0.67\%$
18. Decimal: $0.28$, Percent: $28\%$
19. Decimal: $\approx0.1818$, Percent: $\approx18.18\%$
20. Decimal: $2.8$, Percent: $280\%$
21. Decimal: $\approx0.5556$, Percent: $\approx55.56\%$
22. Decimal: $0.65$, Percent: $65\%$
23. Decimal: $0.08$, Percent: $8\%$
24. Decimal: $\approx3.333$, Percent: $\approx333.3\%$
25. No, the friend is incorrect. $1.475\% = 0.01475$, not $147.5\%$ (they multiplied by 100 instead of dividing by 100).
26. $0.54$
27. $15\%$
28. $88\%$
29. Decimal: $0.86$, Percent: $86\%$
30. $5$ times