SHSAT Sunset

3(0.01) − 3(0.1)

2024 Handbook

2024 Test A Math · Question 51 of 57

Question

3(0.01)−3(0.1)=3(0.01) - 3(0.1) =

  • A−0.33
  • B−0.27
  • C0
  • D0.33
Show the answer

Correct answer: B

3(0.01)−3(0.1)=3(0.01) - 3(0.1) =

0.03−0.3=−0.270.03 - 0.3 = -0.27

Question analysis

This decimal question asks for the value of 3 times 0.01 minus 3 times 0.1. Students multiply each decimal by 3 and subtract, keeping the order of the subtraction as written. The two decimals look alike, so place value and the sign of the result both need care.

NYS standards
  • 7.NS.1c rational number subtraction
  • 6.NS.3 multi-digit decimal operations
Grade level
Grade 7 content, by NYS standard
Compared with grade 7
At grade 7 Grade 7 students subtract rational numbers and get negative results. This short computation adds place-value care, since 0.01 and 0.1 look alike, but it is a routine two-step grade 7 exercise.
Estimated difficulty
Straightforward: two steps or one careful reading.
What makes it hard
Solution
2 steps
Reading level
Question and choices: about grade 16+, 1 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

Two quick multiplications leave 0.03 − 0.3, a subtraction whose result is negative. The usual errors are adding the two products, with or without a minus sign, and treating 0.01 and 0.1 as the same number. Rewriting the subtraction as −(0.3 − 0.03) keeps the place values lined up and makes the sign plain.

  1. Error-prone arithmetic moderate Working it out

    The products 0.03 and 0.3 have their digits in different places, and taking the larger from the smaller crosses zero, so both alignment and sign need care. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

  2. A very close wrong answer minor Choosing the answer

    The choice −0.33 has the right sign and is only 0.06 from the answer, so a sense that the result is a little below zero cannot separate them. (Embretson & Wetzel, 1987; Gorin & Embretson, 2006; Ascalon et al., 2007)

Strategy: Multiply each decimal by 3, then subtract with the place values lined up; or factor out the 3 and compute 3 times (0.01 − 0.1).

Traps

  • Negatives and direction: Arithmetic with negative numbers, the order of a subtraction, or direction on a number line. (Moving a term across the equals sign without changing its sign is a faulty procedure.)
  • Wrong operation: Adds instead of multiplying, divides the wrong way round, turns a ratio or rate upside down, or undoes a step in the wrong direction (subtracts what should be added back).

The wrong answers, classified

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Subtracting a bigger number
a−b=−(b−a)a - b = -(b - a)
a and b are numbers, and b is the bigger one. When you take a bigger number away from a smaller one, the answer is negative. Its size is the gap between them, b minus a. So subtract the other way, then put a minus sign in front.

  1. Sort out the problem

    3(0.01) means 3 times 0.01. A number right next to parentheses means multiply. Then subtract 3 times 0.1. Note that 0.01 is one hundredth, and 0.1 is one tenth. They are not equal. Watch out: treating them as equal makes the two parts cancel to 0, choice C.

  2. Multiply each part

    3×0.01=0.033 \times 0.01 = 0.03

    3×0.1=0.33 \times 0.1 = 0.3

    So the problem is 0.03−0.30.03 - 0.3. Write 0.3 as 0.30 so both have two decimal places. Now you can see that 0.30 is bigger than 0.03.

  3. Subtract the bigger number

    You take a bigger number from a smaller one, so the answer is negative.

    a−b=−(b−a)a - b = -(b - a)

    0.03−0.30=−(0.30−0.03)=−0.270.03 - 0.30 = -(0.30 - 0.03) = -0.27

    Watch out: find the gap between the numbers. Don’t add them. Adding gives 0.33, choice D, or −0.33, choice A.

    So the answer is B, −0.27.

Check your answer

Pull out the 3 first: 3×(0.01−0.1)=3×(−0.09)=−0.273 \times (0.01 - 0.1) = 3 \times (-0.09) = -0.27. Same answer. Also think of a number line. Start at 0.03, just right of 0. Move 0.30 to the left. You land a little left of 0, at −0.27.

More questions like this

The original DOE question

Question 108 as printed on page 89 of the DOE handbook.
As printed in the DOE’s NYC Guide to the Specialized High Schools Admissions Test (SHSAT) for 2025 Admissions, page 89, question 108. Open page 89 of the handbook (PDF) The handbook letters this question’s choices E–H; here they are A–D (E = A, F = B, G = C, H = D).