Practice worksheet featuring exercises on comparing and ordering fractions, decimals, and percentages.

Here are the solutions to the problems on the worksheet.

Question 1

To solve these, it is easiest to change everything into decimals so we can compare them directly. Remember that percent (%) means "out of 100," so you divide by 100. For fractions, divide the top number by the bottom number.

a) $0.35$ vs $32\%$
* Convert $32\%$ to a decimal: $32 \div 100 = 0.32$.
* Compare: $0.35$ is bigger than $0.32$.
* Answer: >

b) $0.4$ vs $4\%$
* Convert $4\%$ to a decimal: $4 \div 100 = 0.04$.
* Compare: $0.4$ (which is $0.40$) is bigger than $0.04$.
* Answer: >

c) $0.2$ vs $\frac{1}{5}$
* Convert $\frac{1}{5}$ to a decimal: $1 \div 5 = 0.2$.
* Compare: They are exactly the same.
* Answer: =

d) $\frac{3}{5}$ vs $0.55$
* Convert $\frac{3}{5}$ to a decimal: $3 \div 5 = 0.6$.
* Compare: $0.6$ is bigger than $0.55$.
* Answer: >

e) $75\%$ vs $\frac{3}{4}$
* Convert $\frac{3}{4}$ to a decimal: $3 \div 4 = 0.75$.
* Convert $75\%$ to a decimal: $0.75$.
* Compare: They are exactly the same.
* Answer: =

f) $0.09$ vs $90\%$
* Convert $90\%$ to a decimal: $90 \div 100 = 0.9$.
* Compare: $0.09$ is smaller than $0.9$.
* Answer: <

***

Question 2

To put these in ascending order (smallest to biggest), convert every number to a decimal first.

a) $70\%, \frac{3}{4}, 0.6, \frac{2}{3}$
* $70\% = 0.70$
* $\frac{3}{4} = 0.75$
* $0.6 = 0.60$
* $\frac{2}{3} \approx 0.67$
* Order from smallest to largest: $0.60, 0.67, 0.70, 0.75$
* Answer: $0.6, \frac{2}{3}, 70\%, \frac{3}{4}$

b) $0.4, \frac{7}{15}, 35\%, \frac{3}{7}$
* $0.4 = 0.400$
* $\frac{7}{15} \approx 0.467$
* $35\% = 0.350$
* $\frac{3}{7} \approx 0.429$
* Order from smallest to largest: $0.350, 0.400, 0.429, 0.467$
* Answer: $35\%, 0.4, \frac{3}{7}, \frac{7}{15}$

c) $0.82, \frac{4}{5}, 85\%, \frac{2}{3}, \frac{7}{8}$
* $0.82 = 0.820$
* $\frac{4}{5} = 0.800$
* $85\% = 0.850$
* $\frac{2}{3} \approx 0.667$
* $\frac{7}{8} = 0.875$
* Order from smallest to largest: $0.667, 0.800, 0.820, 0.850, 0.875$
* Answer: $\frac{2}{3}, \frac{4}{5}, 0.82, 85\%, \frac{7}{8}$

d) $\frac{5}{8}, 0.6, 62\%, \frac{2}{3}, 0.06$
* $\frac{5}{8} = 0.625$
* $0.6 = 0.600$
* $62\% = 0.620$
* $\frac{2}{3} \approx 0.667$
* $0.06 = 0.060$
* Order from smallest to largest: $0.060, 0.600, 0.620, 0.625, 0.667$
* Answer: $0.06, 0.6, 62\%, \frac{5}{8}, \frac{2}{3}$

e) $\frac{8}{9}, 88\%, 0.89, \frac{9}{10}, \frac{7}{8}$
* $\frac{8}{9} \approx 0.889$
* $88\% = 0.880$
* $0.89 = 0.890$
* $\frac{9}{10} = 0.900$
* $\frac{7}{8} = 0.875$
* Order from smallest to largest: $0.875, 0.880, 0.889, 0.890, 0.900$
* Answer: $\frac{7}{8}, 88\%, \frac{8}{9}, 0.89, \frac{9}{10}$

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Final Answer:

Question 1
a) >
b) >
c) =
d) >
e) =
f) <

Question 2
a) $0.6, \frac{2}{3}, 70\%, \frac{3}{4}$
b) $35\%, 0.4, \frac{3}{7}, \frac{7}{15}$
c) $\frac{2}{3}, \frac{4}{5}, 0.82, 85\%, \frac{7}{8}$
d) $0.06, 0.6, 62\%, \frac{5}{8}, \frac{2}{3}$
e) $\frac{7}{8}, 88\%, \frac{8}{9}, 0.89, \frac{9}{10}$