5th Grade Place Value and Powers of Ten Test Solutions and Scoring (PDF)
This powers of ten test answers for 5th Grade covers place value and powers of ten (Common Core 5.NBT.A.1, 5.NBT.A.2), with a free PDF to print.
Use this answer key to grade the powers of 10 test. Every solution names the number of places the decimal point moves. Use the scoring guide for partial credit. The total is 20 points, and 16 or more points shows secure understanding of place value patterns.
Grade 5 · Common Core State Standards: 5.NBT.A.1, 5.NBT.A.2
Powers of ten test answers: worked solutions
Question 1 – Digits in 6,660 [2 pts]
(a) \(6{,}000\div600=10\). 10 times
(b) \(60\div600=\frac{1}{10}\).\(\frac{1}{10}\)
Scoring: 1 point for each correct answer.
Question 2 – Multiply and divide by 10 [2 pts]
(a) One place right: 38
(b) One place left: 52
Scoring: 1 point for each correct answer.
Question 3 – Powers of 10 operations [3 pts]
(a) Two places right: 64
(b) Three places right: 7.1 becomes 7100, 7,100
(c) Two places left: 43
Scoring: 1 point for each correct answer.
Question 4 – Exponents [2 pts]
(a) 10,000 has 4 zeros: \(10^{4}\)
(b) \(10\times10\times10\): 1,000
Scoring: 1 point for each correct answer.
Question 5 – Missing exponents [2 pts]
(a) 2.9 to 2,900 is 3 places right: 3
(b) 8 to 0.08 is 2 places left: 2
Scoring: 1 point for each correct exponent.
Question 6 – Mei's mistake [2 pts]
Mei added two zeros at the end, which does not change the value. Multiplying by 100 moves the decimal point 2 places right.
\(0.35\times100=35\). Correct product: 35
Scoring: 1 point for explaining the mistake (the point must move right), 1 point for 35.
Question 7 – Peach packs [3 pts]
(a) \(6{,}000\div10^{2}=6{,}000\div100=60\). 60 packs
(b) \(60\div10=6\). 6 crates
Scoring: (a) 1 point. (b) 2 points: 1 for dividing 60 by 10, 1 for the answer 6.
Question 8 – Cupcake sale [3 pts]
(a) \(1.25\times10=12.5\): \(\$12.50\)
(b) \(1.25\times100=125\): \(\$125\)
(c) \(1.25\times1{,}000=1{,}250\): \(\$1{,}250\)
Scoring: 1 point for each correct amount. Do not penalize a missing dollar sign twice.
Question 9 – Digits in 0.88 [1 pt]
The 8 in the tenths place is 0.8. The 8 in the hundredths place is 0.08.
\(0.08\div0.8=\frac{1}{10}\).
Answer: \(\frac{1}{10}\)
Scoring: 1 point for 1/10 (or one tenth).
Total score
20 points
Key facts behind this powers of ten test answers
- Each place is 10 times the place to its right and 1/10 of the place to its left.
- The exponent of a power of 10 tells how many 10s are multiplied and how many zeros the value has.
- Multiplying by a power of 10 moves the decimal point right by the exponent.
- Dividing by a power of 10 moves the decimal point left by the exponent.
- 10 to the third power means 10 × 10 × 10 = 1,000, not 3 × 10.
How to use this powers of ten test answers
Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.
All Grade 5 chapters: Grade 5 math.
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