The decimal 0.06 can be written as the fraction x/50 . What is the value of x ?

The decimal 0.06 can be written as the fraction

2018 Handbook

2018 Test B Math · Question 47 of 57

Also in 2026 Practice Test B Math, question 1; 2025 Practice Test B Math, question 2.

Question

The decimal 0.06 can be written as the fraction $\frac{x}{50}$ . What is the value of $x$ ?

Show the answer

Correct answer: A

$0.06=\frac{6}{100}$

Simplify the fraction to find the answer:

$\frac{6}{100}=\frac{3}{50}$

$x=3$

Question analysis

This question asks students to rewrite the decimal 0.06 as an equivalent fraction with a denominator of 50 and give the missing numerator. It tests converting between decimals and fractions. The step that trips students up is moving from hundredths to fiftieths, which means scaling the numerator in the right direction.

NYS standards: 6.NS.3 multi-digit decimal operations
Grade level: Grade 6 content, by NYS standard
Compared with grade 7: Below grade 7 Converting a decimal to an equivalent fraction is upper elementary and grade 6 work. This is a single routine conversion with no context and no traps beyond a place-value slip, well below grade 7 demand.
Estimated difficulty: Routine: one familiar step, little to misread.
Thinking it demands: Depth of knowledge 1, recall and reproduction · mainly apply
What makes it hard: Error-prone arithmetic minor
Solution: 2 steps
Reading level: Question and choices: about grade 6, 15 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

A one-idea question: write 0.06 as a fraction and rename it with a denominator of 50. The only real risk is keeping the 6 when the denominator changes, or scaling the numerator in the wrong direction. Checking that 3 ÷ 50 really gives 0.06 settles it.

Error-prone arithmetic minor Working it out
The decimal is in hundredths but the target denominator is 50, so the numerator has to be halved along with the denominator rather than kept as 6. (Brown & Burton, 1978; Junker & Sijtsma, 2001)

Strategy: Write the decimal as a fraction over 100, then find the equivalent fraction over 50 by dividing numerator and denominator by the same number.

Traps

Stops one step early: A choice is a number from partway through the solution.

The wrong answers, classified

B Stops one step early (King et al., 2004; Gierl et al., 2017)
Reveals partial knowledge Expected pull: strong
Writes 0.06 as 6/100 and keeps 6 as the numerator even though the denominator has changed from 100 to 50.
C Wrong operation (Hegarty, Mayer & Monk, 1995; King et al., 2004)
Reveals a misconception Expected pull: moderate
Doubles the 6 instead of halving it, scaling the numerator up while the denominator goes down from 100 to 50.
D An arithmetic slip (Junker & Sijtsma, 2001)
Reveals a slip Expected pull: weak
Reads 0.06 as 0.6 and multiplies by 50, a decimal-place slip that makes the numerator ten times too large.

How the questions are analyzed, and the research behind it

Worked solution, step by step

Formulas used

Equivalent fractions: $\frac{a}{b} = \frac{a \div k}{b \div k}$; a is the top number and b is the bottom number. k is any number that divides both. Dividing the top and bottom by the same number keeps the value the same. Use it to give a fraction a new bottom number.

Sort out the question
You need to write 0.06 as a fraction with 50 on the bottom. The top number of that fraction is $x$ . You need to find $x$ .
Write the decimal as a fraction
0.06 has two digits after the decimal point. That means it counts hundredths. So 0.06 is six hundredths.
$0.06 = \frac{6}{100}$
Change the bottom to 50
To turn 100 into 50, divide by 2. The rule for equivalent fractions says to do the same to the top.
$\frac{6}{100} = \frac{6 \div 2}{100 \div 2} = \frac{3}{50}$
So $x = 3$ .
Watch out: the 6 must change too. Keeping the 6 gives choice B. Doubling it to 12 gives choice C.
Give the answer
The fraction $\frac{3}{50}$ is the same amount as 0.06, and its top number is 3. So the answer is A, 3.

Check your answer

Divide to turn the fraction back into a decimal: $3 \div 50 = 0.06$ . You can also multiply: $0.06 \times 50 = 3$ . Both match. Choice D, 30, comes from reading 0.06 as 0.6.

The original DOE question

Question 104 as printed on page 162 of the DOE handbook. — As printed in the DOE’s Specialized High Schools Student Handbook 2018–2019, page 162, question 104. Open page 162 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).