Middle School Math Quiz: Estimating Decimals And Percents

9 questions · exam conditions

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Estimating Decimals And PercentsQuestion 1 of 9

A store marks up items by $40\%$ above wholesale cost. During a sale, they offer $25\%$ off the retail price. If an item costs $60 wholesale, approximately what profit does the store make during the sale?

$12

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Middle School Math Quiz

Middle School Math Quiz: Estimating Decimals And Percents

Practice Estimating Decimals And Percents in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Estimating Decimals And Percents, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$3
$6
$9 (correct answer)
$12

Explanation: Wholesale cost: $60. For estimation, round the $

40\%

markup to

50\%

: Retail price ≈

\

60 \times 1.5 = $90

. Sale price:

$90 \times 0.75 = $67.50

. Profit:

$67.50 - $60 = $7.50 ≈ $9

. Choice A uses exact calculations without rounding. Choice B underestimates the markup. Choice D overestimates the final profit.

Question 2

A investment account loses $15.3\%$ of its value in the first year, then gains $18.7\%$ in the second year. If the account started with $8,500, approximately what is its value after two years?

$8,200
$8,500
$8,800 (correct answer)
$9,100

Explanation: Round to

15\%

loss and

19\%

gain on $8,500. After year 1: $

\

8,500 \times 0.85 \approx $7,225

. After year 2:

$7,225 \times 1.19 \approx $8,598

, closest to $8,800. Choice A stops after the first year loss. Choice B assumes the changes cancel out. Choice D adds the percentages linearly to the original amount.

Question 3

In a chemistry lab, a solution is $0.0847$ molar concentration. If you need to dilute it to $65\%$ of its original concentration and you start with $250$ mL, approximately how much water should you add?

$130$ mL (correct answer)
$140$ mL
$150$ mL
$160$ mL

Explanation: For dilution, if final concentration is

65\%

of original, then

C_1V_1 = C_2V_2

gives us

250 \text{ mL} = 0.65 \times V_2

, so

V_2 = \frac{250}{0.65} \approx \frac{250}{0.65} \approx 385

mL total volume. Water to add:

385 - 250 = 135

mL, closest to

130

mL. Choice B uses

\frac{250}{0.6}

. Choice C uses

250 \times 0.6

. Choice D uses

250 \times 0.65

Question 4

In a recent survey, $0.237$ of respondents preferred brand A, $0.184$ preferred brand B, and the rest were undecided. If there were $1,847$ total respondents, approximately how many more people preferred brand A than brand B?

$98$ people (correct answer)
$106$ people
$115$ people
$123$ people

Explanation: Estimate by rounding:

1,847 \approx 1,800

and

0.237 - 0.184 = 0.053 \approx 0.05

. So the difference is about

0.05 \times 1,800 = 90

people, closest to

98

. Choice B uses exact decimals with rounded population. Choice C uses original population with rounded difference. Choice D uses both exact values.

Question 5

A restaurant bill comes to $47.83 before tax. The tax rate is $ $8.25\%$ $and you want to leave a$ $18\%$ $ tip on the pre-tax amount. Which of the following is the best estimate for the total amount you will pay?

$58
$62 (correct answer)
$66
$70

Explanation: To estimate: Round $47.83 to $48. Tax is about $

8\% \times \

48 = $3.84 \approx $4

. Tip is about

18% \times $48 = $8.64 \approx $9

. Total:

$48 + $4 + $9 = $61 \approx $62

. Choice A forgets either tax or tip. Choice C uses tip on post-tax amount. Choice D overestimates both percentages significantly.

Question 6

The price of gasoline increased from $3.47 per gallon to $4.23 per gallon over six months. What is the best estimate for the percent increase?

$18\%$
$30\%$
$26\%$
$22\%$ (correct answer)

Explanation: When you encounter percent increase problems, you're finding how much a quantity has grown relative to its original value. The formula is: percent increase =

\frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%

. Here, gasoline increased from $3.47 to $4.23. The change is $

\

4.23 - $3.47 = $0.76

. So the percent increase is

\frac{0.76}{3.47} \times 100%

. To estimate this quickly, round

3.47 to

3.50 and

0.76 to

0.75. Now you have

\frac{0.75}{3.50} = \frac{3}{14} \approx 0.21 = 21%

. This is closest to

22%

, making D the correct answer. Choice A (

18%

) is too low—it underestimates the substantial price jump. Choice B (

30%

) represents a common error where students might incorrectly calculate

\frac{0.76}{4.23}

using the new price as the denominator instead of the original price. Choice C (

26%

) could result from rounding errors or miscalculation, perhaps from estimating

\frac{0.76}{3.00}

instead of using the actual denominator. For percent increase problems, always remember: divide the change by the original amount, not the new amount. Practice estimating by rounding to friendly numbers—turning

\frac{0.76}{3.47}

into

\frac{3}{14}

makes the mental math much easier and gets you close enough to identify the right answer choice.

Question 7

A recipe calls for $2.75$ cups of flour, but you want to make $130\%$ of the recipe. You only have a $\frac{1}{3}$ cup measuring tool. Approximately how many scoops will you need?

$10$ scoops
$13$ scoops
$12$ scoops
$11$ scoops (correct answer)

Explanation: This problem combines three key pre-algebra skills: converting percentages to decimals, multiplying decimals, and dividing fractions. When you see a recipe scaling problem, break it down into clear steps. First, calculate how much flour you need for 130% of the recipe. Convert the percentage:

130\% = 1.30

. Then multiply:

2.75 \times 1.30 = 3.575

cups of flour. Next, determine how many

\frac{1}{3}

-cup scoops you need by dividing:

3.575 \div \frac{1}{3}

. To divide by a fraction, multiply by its reciprocal:

3.575 \times 3 = 10.725

scoops. Since you can't make partial scoops when measuring, you need to round up to 11 complete scoops. Looking at the wrong answers: Choice A (10 scoops) gives you

10 \times \frac{1}{3} = 3.33

cups, which is slightly less than the 3.575 cups needed. Choice B (13 scoops) likely comes from incorrectly rounding 10.725 to the nearest whole number above 12, or from calculation errors. Choice C (12 scoops) results from rounding 10.725 to the nearest whole number instead of considering that you need at least enough flour, so you must round up to ensure you have sufficient ingredients. Remember: in cooking problems involving measurements, always round up when the exact amount falls between whole measuring units. You want to have enough ingredients, and having slightly more is better than running short mid-recipe.

Question 8

A factory produces widgets at a rate where $12.7\%$ are defective. If the factory aims to ship $2,450$ non-defective widgets, approximately how many total widgets must they produce?

$2,750$ widgets
$2,800$ widgets (correct answer)
$2,900$ widgets
$3,100$ widgets

Explanation: If

12.7\%

are defective, then

87.3\%

are good. Round to

87\%

good and

2,450

2,500

. We need

0.87x = 2,500

, so

x \approx 2,500 \div 0.87 \approx 2,500 \div 0.9 \approx 2,778

, closest to

2,800

. Choice A adds the defective amount incorrectly. Choice C uses

85\%

good rate. Choice D significantly overestimates the defective rate impact.

Question 9

A baseball player's batting average dropped from $0.347$ to $0.298$ during a slump. By approximately what percent did their batting average decrease?

$14\%$ (correct answer)
$16\%$
$18\%$
$20\%$

Explanation: Round

0.347

0.35

and

0.298

0.30

. The decrease is

0.05

. Percent decrease =

\frac{0.05}{0.35} \times 100\% \approx 14.3\%

, closest to

14\%

. Choice B uses

\frac{0.05}{0.30}

(wrong denominator). Choice C uses the difference

0.049

without proper context. Choice D uses

\frac{0.05}{0.25}

from misreading.