8th Grade Scientific Notation Test Solutions and Scoring (PDF)

8th Grade math test solutions: Scientific Notation – Maths PDF

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This scientific notation test answers for 8th Grade covers scientific notation (Common Core 8.EE.A.3, 8.EE.A.4), with a free PDF to print.

Use this answer key to score the scientific notation test out of 20 points. Each solution shows the full work and a scoring guide, so partial credit can be given fairly when a student shows correct steps but makes an arithmetic slip.

Grade 8 · Common Core State Standards: 8.EE.A.3, 8.EE.A.4

Scientific notation test answers: worked solutions

Question 1 – Write in scientific notation [2 pts]

\(5.8 \times 10^{7}\)
\(4.7 \times 10^{-6}\)

Scoring: 1 point each.

Question 2 – Write in standard form [2 pts]

\(30{,}600\)
\(0.00008\)

Scoring: 1 point each.

Question 3 – Compare sizes [2 pts]

Exponents: -5, -2, 2.

The order is C, A, B.

\(4 \times 10^{-5},\ 3 \times 10^{-2},\ 8 \times 10^{2}\)

Scoring: 2 points for the correct order; 1 point if one value is misplaced.

Question 4 – Multiply and divide [3 pts]

\(24 \times 10^{8} = 2.4 \times 10^{9}\)
\(3 \times 10^{5}\)

Scoring: Part a: 1 point for \(24 \times 10^{8}\), 1 point for \(2.4 \times 10^{9}\). Part b: 1 point.

Question 5 – Add [2 pts]

\(3.1 \times 10^{4} = 0.31 \times 10^{5}\).

\(2.4 + 0.31 = 2.71\).

\(2.71 \times 10^{5}\)

Scoring: 1 point for matching the exponents. 1 point for the sum.

Question 6 – Sun and Jupiter [3 pts]

\(4.8 \times 10^{8} = 48 \times 10^{7}\).

\(48 \times 10^{7} – 9.3 \times 10^{7} = 38.7 \times 10^{7} = 3.87 \times 10^{8}\).

\(3.87 \times 10^{8}\) miles

Scoring: 1 point for matching exponents, 1 point for 38.7, 1 point for scientific notation.

Question 7 – Cells across a millimeter [3 pts]

Many cells fit in 1 mm.

\(\frac{10^{-3}}{2.5 \times 10^{-5}} = 0.4 \times 10^{2} = 4 \times 10^{1}\).

40 cells

Scoring: 1 point for setting up a quotient, 1 point for the exponent work, 1 point for 40.

Question 8 – Explain [3 pts]

No, the front number 0.5 is less than 1. \(0.5 \times 10^{6} = 5 \times 10^{5}\).

Standard form: 500,000.

Scoring: 1 point for the explanation, 1 point for \(5 \times 10^{5}\), 1 point for 500,000.

Total score

Total

20 points

Key facts behind this scientific notation test answers

Key facts

Form: \(a \times 10^{n}\) with \(1 \le a < 10\).
\(93{,}000{,}000 = 9.3 \times 10^{7}\) and \(0.00032 = 3.2 \times 10^{-4}\).
To multiply, multiply the front numbers and add the exponents; to divide, subtract the exponents.
To add or subtract, first write both numbers with the same power of 10.
To tell how many times as large one value is, divide the two values.

How to use this scientific notation 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 8 chapters: Grade 8 math.

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