5th Grade Reading, Comparing and Rounding Decimals Test Solutions and Scoring (PDF)

Use this answer key to grade the decimals test. Each solution shows the place value reasoning, and the scoring guide lists partial credit. The total is 20 points. Accept equivalent word forms and any correct expanded form that the question allows.
Grade 5 · Common Core State Standards: 5.NBT.A.3, 5.NBT.A.4
Question 1 – Write in words [2 pts]
(a) seventy-five thousandths
(b) twelve and four hundredths
Scoring: 1 point for each correct word form.
Question 2 – Write as decimals [2 pts]
(a) 6.09
(b) 0.205
Scoring: 1 point for each correct decimal.
Question 3 – Expanded form [2 pts]
\(4\times1+3\times\frac{1}{10}+7\times\frac{1}{100}+2\times\frac{1}{1000}\)
Scoring: 2 points for all four terms correct. 1 point for three correct terms, or for decimals (4 + 0.3 + 0.07 + 0.002) instead of fractions.
Question 4 – Value of a digit [2 pts]
(a) The 5 is in the hundredths place: \(0.05\)
(b) The 1 is in the thousandths place: \(0.001\)
Scoring: 1 point for each correct value.
Question 5 – Compare decimals [3 pts]
(a) 0.70 > 0.07: >
(b) 3.405 < 3.450: <
(c) 8.60 = 8.6: =
Scoring: 1 point for each correct symbol.
Question 6 – Order decimals [2 pts]
Write with three places: 5.090, 5.900, 5.095, 5.190.
Greatest to least: 5.900, 5.190, 5.095, 5.090.
Answer: \(5.9, 5.19, 5.095, 5.09\)
Scoring: 2 points for the correct order. 1 point if only one pair is in the wrong order.
Question 7 – Round 7.4851 [3 pts]
(a) The tenths digit is 4, so round down: 7
(b) The hundredths digit is 8, so round up: 7.5
(c) The thousandths digit is 5, so round up: 7.49
Scoring: 1 point for each correct rounding.
Question 8 – Long jump [3 pts]
Write with three places: 13.250, 13.300, 13.205.
(a) 13.3 ft (jump 2)
(b) \(13.205, 13.25, 13.3\)
(c) 13.205 has hundredths digit 0, so it rounds to 13.2 ft.
Scoring: 1 point for each part.
Question 9 – Priya's rounding [1 pt]
The tenths digit is 4, which is less than 5. Round down: 3.46 rounds to 3.
Answer: No, the answer is 3
Scoring: 1 point for “no” with a correct reason.
20 points
All Grade 5 chapters: Grade 5 math.
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