Jevon earns 1/2% per year

2024 Handbook

2024 Test B Math · Question 42 of 57

Question

Jevon earns $\frac{1}{2}\%$ per year on the money in his savings account. Which expression is not another way to write $\frac{1}{2}\%$ ?

A $\frac{0.005}{100}$
B $\frac{\frac{1}{2}}{100}$
C $\frac{5}{1{,}000}$
D $\frac{1}{200}$

Show the answer

Correct answer: A

Rewrite the percent as a decimal:

$\frac{1}{2}\%=0.5\%=0.005$

So the correct answer must not equal 0.005:

Option A

$\frac{0.005}{100}=0.00005$

Option B

$\frac{\frac{1}{2}}{100}=0.5\div 100=0.005$

Option C

$\frac{5}{1{,}000}=0.005$

Option D

$\frac{1}{200}=0.005$

All answer options except Option A equal 0.005. Therefore, Option A is the correct answer.

Question analysis

Jevon's savings account earns one-half percent a year, and students must find the expression that is not another way to write one-half percent. It tests converting a percent less than 1 into fractions and decimals. Reading the word not carefully, and evaluating each stacked or unfamiliar fraction correctly, are what make it tricky.

NYS standards: 6.RP.3c percent as a rate per 100
7.NS.2d fractions to decimals by long division
Grade level: Grade 7 content, by NYS standard
Compared with grade 7: At grade 7 Converting between percents, fractions and decimals is grade 6 and 7 work. A percent smaller than 1 is less familiar, and the question asks which form is not equal, so all four must be checked, which keeps it at typical grade 7 demand.
Estimated difficulty: Moderate: several steps, or a close reading with one strong distractor.
Thinking it demands: Depth of knowledge 1, recall and reproduction · mainly apply
What makes it hard: A question in the negative moderate
Every choice must be checked moderate
Error-prone arithmetic minor
Solution: 3 steps
Reading level: Question and choices: about grade 7, 25 words.
Students, last 30 days: Not enough answers yet to show (it takes 10).

Why it is hard, traps and wrong answers (shows the answer)

Why it is hard

Every expression is built from the same idea, so the question tests whether students can convert a percent smaller than 1 without losing track of decimal places. The odd one out, 0.005 over 100, looks like a correct form, because 0.005 is one-half percent and dividing by 100 seems to turn it into a percent. Converting one-half percent to 0.005 once and comparing each expression with it beats reasoning about each form.

A question in the negative moderate Understanding the question
The bold word not asks for the one expression unequal to one-half percent, so the three expressions that check out are exactly the ones to reject. (Haladyna, Downing & Rodriguez, 2002)
Every choice must be checked moderate Choosing the answer
Three of the four forms are equal, so each has to be converted to a decimal and compared with 0.005 before the odd one out can be named. (Embretson & Wetzel, 1987)
Error-prone arithmetic minor Working it out
One-half percent is 0.5 with the point moved two places, 0.005, and dividing that by 100 moves it two more places, to 0.00005. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Write one-half percent as a single decimal by dividing one half by 100, then evaluate each expression as a decimal and compare it with that value.

Traps

NOT, LEAST or EXCEPT: The question asks for the exception, the least, or what is not true.
Answer in another form: The right answer is written differently from the way you worked it out.

The wrong answers, classified

B Misreads the question (Hegarty, Mayer & Monk, 1995)
Reveals a slip Expected pull: moderate
Misses the bold not and picks the expression that equals one-half percent most plainly, one half over 100, the literal meaning of percent.
C Misunderstands the concept (Smith, diSessa & Roschelle, 1993; De Bock et al., 1998; Ni & Zhou, 2005)
Reveals a misconception Expected pull: weak
Believes a percent must be written over 100, so 5 over 1,000 looks like a different number, though both equal 0.005.
D An arithmetic slip (Junker & Sijtsma, 2001)
Reveals a slip Expected pull: moderate
Divides 1 by 200 and misplaces the decimal point, getting 0.05 instead of 0.005, so 1/200 seems not to equal one-half percent.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Percent as a fraction: $p\% = \frac{p}{100}$; p is any number. The % sign means out of 100. So p percent is p divided by 100. Dividing by 100 moves the decimal point two places to the left.

Sort out the question
The question asks which expression is not equal to $\frac{1}{2}\%$ . So three choices are equal to it, and one is different. You need the odd one out.
Write the percent as a decimal
One half is 0.5. A percent means out of 100, so divide by 100.
$\frac{1}{2}\% = 0.5\% = \frac{0.5}{100} = 0.005$
So $\frac{1}{2}\%$ is 0.005. It is half of one percent, a very small amount.
Test each choice
Turn each choice into a decimal. Then compare it with 0.005.
Choice Work it out Equal to 0.005?
A $0.005 \div 100 = 0.00005$ No
B $0.5 \div 100 = 0.005$ Yes
C $5 \div 1{,}000 = 0.005$ Yes
D $1 \div 200 = 0.005$ Yes
Pick the one that is different
Choice A divides by 100 twice. The 0.005 was already divided by 100 once. Dividing again makes it 100 times too small.
Watch out: Choice B is the plainest way to write $\frac{1}{2}\%$ : one half over 100. Picking it means missing the word “not.” Also, 1 ÷ 200 is 0.005, not 0.05, so D is equal too.
So the answer is A, $\frac{0.005}{100}$ .

Choice	Work it out	Equal to 0.005?
A	$0.005 \div 100 = 0.00005$	No
B	$0.5 \div 100 = 0.005$	Yes
C	$5 \div 1{,}000 = 0.005$	Yes
D	$1 \div 200 = 0.005$	Yes

Check your answer

Use fractions instead. Half of one hundredth is $\frac{1}{2} \times \frac{1}{100} = \frac{1}{200}$ , which is choice D. And $\frac{5}{1{,}000}$ simplifies to $\frac{1}{200}$ too. Only A is a different amount.

The original DOE question

Question 99 as printed on page 211 of the DOE handbook. — As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 211, question 99. Open page 211 of the handbook (PDF)