Grade 8 Percent as a Number: Unit Mastery Quiz with Full Solutions

Position in the unit

This record is an end-of-unit assessment for Grade 8: Number -> Decimals and Percents -> Percent as a Number.

Use this quiz after instruction and practice on the core idea that a percent is a number per hundred. Do not use it as the first teaching record for the topic.

Related records:

• rea.m08.number.ratios-rates-proportions.percent-bridges.unit-mastery-quiz for broader conversion work among percent, decimal, fraction, and ratio forms.
• rea.m08.number.ratios-rates-proportions.equivalent-ratios.unit-mastery-quiz for proportional reasoning that supports some percent thinking.
• rea.m08.number.integer-operations.add-subtract.unit-mastery-quiz as a model of mixed numerical and error-analysis assessment structure.

Quiz design

• Level: Grade 8
• Questions: 10
• Suggested time: 25-35 minutes
• Total marks: 20
• Calculator: Not required

What this quiz assesses

A student shows mastery if they can:

• interpret percent as "out of 100"
• convert between percent and decimal forms
• compare percents greater than, less than, and equal to 100%
• locate percent values on a number line
• use percent language correctly in simple contexts
• detect and correct common percent errors

Unit Mastery Quiz

Question 1 (2 marks)

Write each percent as a decimal.

a) 7%
b) 45%
c) 125%
d) 0.8%

Question 2 (2 marks)

Write each decimal as a percent.

a) 0.6
b) 0.03
c) 1.4
d) 0.085

Question 3 (2 marks)

Order these from least to greatest:

5%, 0.5%, 50%, 105%, 15%

Show enough work to justify the order.

Question 4 (2 marks)

Place these values on a number line from 0 to 150:

20%, 75%, 100%, 130%

A full-size drawing is not required. State the positions clearly.

Question 5 (2 marks)

For each statement, write true or false.

a) 34% means 34 out of 100.
b) 150% is impossible because percent cannot be more than 100.
c) 0.25 and 25% represent the same number.
d) 8% is greater than 0.8.

Question 6 (2 marks)

Fill in the blanks.

a) 1% = ______ as a decimal
b) 10% = ______ as a decimal
c) 100% = ______ as a decimal
d) 250% = ______ as a decimal

Question 7 (2 marks)

A water bottle is filled to 80% of its capacity. Another identical bottle is filled to 95% of its capacity.

How much greater is the fill level of the second bottle, in percentage points?

Question 8 (2 marks)

A student says:

"42% means 42 divided by 10, so 42% = 4.2."

Explain the mistake and give the correct value.

Question 9 (2 marks)

Shade interpretation without drawing:

If a 10 by 10 grid represents one whole, what percent is shaded if 37 small squares are shaded? What decimal does that represent?

Question 10 (2 marks)

Choose the better buy statement and justify numerically:

Store A says an item is priced at 65% of the original price.
Store B says an item is priced at 0.72 of the original price.

Which store offers the lower final price?

Marking Key

• Q1: 0.5 mark each
• Q2: 0.5 mark each
• Q3: 2 marks
• Q4: 2 marks
• Q5: 0.5 mark each
• Q6: 0.5 mark each
• Q7: 2 marks
• Q8: 2 marks
• Q9: 2 marks
• Q10: 2 marks

Total: 20 marks

Full Solutions

Question 1

To change a percent to a decimal, divide by 100.

a) 7% = 7/100 = 0.07
b) 45% = 45/100 = 0.45
c) 125% = 125/100 = 1.25
d) 0.8% = 0.8/100 = 0.008

Answer: a) 0.07, b) 0.45, c) 1.25, d) 0.008

Question 2

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

a) 0.6 x 100 = 60%
b) 0.03 x 100 = 3%
c) 1.4 x 100 = 140%
d) 0.085 x 100 = 8.5%

Answer: a) 60%, b) 3%, c) 140%, d) 8.5%

Question 3

Convert all values to comparable percent form:

• 5% = 5%
• 0.5% = 0.5%
• 50% = 50%
• 105% = 105%
• 15% = 15%

Now order from least to greatest: 0.5% < 5% < 15% < 50% < 105%

Answer: 0.5%, 5%, 15%, 50%, 105%

Question 4

Interpret each percent as a number on the 0 to 150 scale.

• 20% is at 20
• 75% is at 75
• 100% is at 100
• 130% is at 130

From left to right on the number line: 20%, 75%, 100%, 130%

Answer: positions 20, 75, 100, and 130 on a 0-150 percent scale

Question 5

a) 34% means 34 out of 100. This is the definition of percent. True
b) Percent can be greater than 100 when the amount is more than one whole. False
c) 25% = 25/100 = 0.25. True
d) 8% = 0.08, and 0.8 = 80%, so 8% is not greater. False

Answer: a) True, b) False, c) True, d) False

Question 6

a) 1% = 1/100 = 0.01
b) 10% = 10/100 = 0.1
c) 100% = 100/100 = 1
d) 250% = 250/100 = 2.5

Answer: a) 0.01, b) 0.1, c) 1, d) 2.5

Question 7

Compare the two fill levels: 95% - 80% = 15%

Because both numbers are already percents, the difference is 15 percentage points.

Answer: 15 percentage points

Question 8

The mistake is using division by 10 instead of division by 100.

Percent means per hundred, not per ten. So: 42% = 42/100 = 0.42

The incorrect answer 4.2 is actually 420%, not 42%.

Answer: The student divided by 10 instead of 100; the correct value is 0.42.

Question 9

A 10 by 10 grid has 100 equal squares. If 37 squares are shaded, then the shaded part is: 37/100 = 37%

As a decimal: 37% = 0.37

Answer: 37% and 0.37

Question 10

Store A: 65% of original price = 0.65 of original price
Store B: 0.72 of original price = 72% of original price

Compare final-price multipliers: 0.65 < 0.72

So Store A gives the lower final price.

Answer: Store A, because paying 65% of the original price is less than paying 72% of the original price.

Mastery threshold recommendation

Recommend mastery at 16/20 or higher, with these two conditions:

• the learner must correctly answer at least 3 of the 4 direct conversion clusters across Questions 1, 2, 5, and 6
• the learner must earn at least 3 of the 4 marks available on the reasoning/application questions: Questions 8, 9, and 10

This threshold is appropriate because percent-as-number work in Grade 8 requires both:

• fluency with conversion and comparison
• meaning: understanding percent as a number out of 100, including values above 100%

Diagnostic interpretation

• 18-20 marks: strong unit mastery; ready to extend into richer percent problems and mixed-form conversion work
• 16-17 marks: secure core mastery; minor review only
• 12-15 marks: partial mastery; reteach decimal-percent conversion and percent greater than 100
• 0-11 marks: not yet secure; return to lesson and guided practice before moving on

Common error patterns to watch for

• Dividing or multiplying by 10 instead of 100
• Thinking percent cannot be greater than 100
• Confusing 0.8 with 8%
• Treating a difference in percents carelessly instead of comparing the numbers directly

For extended conversion practice beyond this quiz, route the learner to rea.m08.number.ratios-rates-proportions.percent-bridges.unit-mastery-quiz.