Question

1. in this section we introduced percent, which means \per centum\ or \per 100\.
2. the number 1 written as a percent is 100%.
3. to change a percent to a decimal, move the decimal point 2 places to the left. drop the % symbol.
4. to change a decimal to a percent, move the decimal point 2 places to the right. add the % symbol at the end of the number.

write each fraction as a percent.

1. $\frac{45}{100}=45\\%$ 6. $\frac{48}{100}=48$ 7. $\frac{7}{100}=$ 8. $\frac{9}{100}=$ 9. $\frac{80}{100}=$
2. $\frac{245}{100}=245\\%$ 12. $\frac{110}{100}=110\\%$ 13. $\frac{5.3}{100}=5.3\\%$ 14. $\frac{8.3}{100}=8.3\\%$ 15. $\frac{0.6}{100}=$

write a percent to express each of the following.

1. 29 out of 100 power boats had a radar navigation system.
2. 13 out of 100 students in the class
3. 78 out of 100 new car owners were satisfied with their purchase.
4. 64 out of 100 college sophomores are their selection of a major. 64%
5. 32 out of 100 people who ate out chose to eat at a fast - food restaurant.

%→decimal
write each percent as a decimal.

1. 51% 24. 42% 25. 7% 26. 6% 27. 20% 28. 40% 29. 43.6% 0.436
2. 0.3% 32. 0.9% 33. 0.72% 34. 0.61% 35. 126% 36. 175% 37. 366%

write each decimal as a percent.

1. 0.74 40. 0.66 41. 0.50 42. 0.40 43. 0.08 44. 0.03 45. 0.56
2. 0.002 48. 0.009 49. 0.0057 50. 0.0026 51. 1.35 52. 1.86 53. 2.72
3. bob paid 0.27 of his income for federal income tax.
4. sally spends 0.31 of her income for

Explanation:

Step1: Recall percent - decimal conversion rules

To convert a percent to a decimal, move the decimal point 2 places to the left and drop the % symbol. To convert a decimal to a percent, move the decimal point 2 places to the right and add the % symbol. For fractions with denominator 100, the numerator is the percentage value.

Step2: Convert fractions to percents

For $\frac{45}{100}$, since the denominator is 100, it is $45\%$. Similarly, $\frac{48}{100}=48\%$, $\frac{7}{100} = 7\%$, $\frac{9}{100}=9\%$, $\frac{80}{100}=80\%$, $\frac{245}{100}=245\%$, $\frac{110}{100}=110\%$, $\frac{5.3}{100}=5.3\%$, $\frac{8.3}{100}=8.3\%$, $\frac{0.6}{100}=0.6\%$.

Step3: Convert ratios to percents

For "29 out of 100 power - boats", it is $29\%$. "13 out of 100 students" is $13\%$, "78 out of 100 new car owners" is $78\%$, "32 out of 100 people" is $32\%$, "64 out of 100 college sophomores" is $64\%$, "8 out of 100 people" is $8\%$.

Step4: Convert percents to decimals

$51\%=\frac{51}{100}=0.51$, $42\% = 0.42$, $7\%=0.07$, $6\%=0.06$, $20\%=0.20 = 0.2$, $40\%=0.40=0.4$, $43.6\%=0.436$, $0.3\%=\frac{0.3}{100}=0.003$, $0.9\%=\frac{0.9}{100}=0.009$, $0.72\%=\frac{0.72}{100}=0.0072$, $0.61\%=\frac{0.61}{100}=0.0061$, $126\%=\frac{126}{100}=1.26$, $175\%=\frac{175}{100}=1.75$, $366\%=\frac{366}{100}=3.66$.

Step5: Convert decimals to percents

$0.74 = 74\%$, $0.66=66\%$, $0.50 = 50\%$, $0.40=40\%$, $0.08 = 8\%$, $0.03=3\%$, $0.56 = 56\%$, $0.002=0.2\%$, $0.009 = 0.9\%$, $0.0057=0.57\%$, $0.0026=0.26\%$, $1.35 = 135\%$, $1.86=186\%$, $2.72=272\%$.

Answer:

The conversions are shown in the step - by - step explanations above for all the given fractions, ratios, percents and decimals.