Question

match the following decimals and percents below.
10 19
11 0.9
12 0.09
13 0.99
14 1.09
15 0.009
a packing box is filled $\frac{4}{5}$ of the way with packing peanuts. what decimal represents the fraction of the box filled with packing peanuts?
17 marcy lives 1.15 miles away from her grandma. what fraction represents the distance between marcys house and her grandmas?
18 nineteen of the 20 students in mrs. gonzalezs science class are attending the field trip. what decimal best represents the portion of the class that attends the trip?
19 the store is marking their price up 145%. what fraction best represents 145%?
20 a student receives a 95% on their math test. which of the follow values are equivalent to 95%? circle all that apply.
a) 95 b) 0.95 c) $\frac{19}{20}$ d) $\frac{95}{100}$

Explanation:

Step1: Convert decimals to percents

To convert a decimal to a percent, multiply by 100.

1. No decimal value given for 10 in the problem - seems to be a formatting issue. Skipping this one.
2. For 0.9, $0.9\times100 = 90\%$, so it matches e) 90%.
3. For 0.09, $0.09\times100=9\%$, so it matches f) 9%.
4. For 0.99, $0.99\times 100 = 99\%$, so it matches b) 99%.
5. For 1.09, $1.09\times100 = 109\%$, so it matches a) 109%.
6. For 0.009, $0.009\times100=0.9\%$, so it matches c) 0.9%.

Step2: Convert fraction to decimal

For 16, to convert $\frac{4}{5}$ to a decimal, divide 4 by 5. $4\div5 = 0.8$.

Step3: Convert decimal to fraction

For 17, 1.15 can be written as $\frac{115}{100}$, and simplifying gives $\frac{23}{20}$.

Step4: Calculate decimal from fraction

For 18, 19 out of 20 students attending. $\frac{19}{20}=19\div20 = 0.95$.

Step5: Convert percent to fraction

For 19, 145% can be written as $\frac{145}{100}$, and simplifying gives $\frac{29}{20}$.

Step6: Find equivalent values for 95%

For 20, 95% is equivalent to 0.95 ($95\div100 = 0.95$) and $\frac{95}{100}=\frac{19}{20}$, so b) 0.95, c) $\frac{19}{20}$, d) $\frac{95}{100}$ are equivalent.

Answer:

1. e) 90%
2. f) 9%
3. b) 99%
4. a) 109%
5. c) 0.9%
6. 0.8
7. $\frac{23}{20}$
8. 0.95
9. $\frac{29}{20}$
10. b) 0.95, c) $\frac{19}{20}$, d) $\frac{95}{100}$