Scientific Notation: Grade 8 Math Test Answer Key – PDF Download

Question 1: Large numbers (2 points)

1. The point moves 7 places left: \(9.3\times 10^{7}\).
2. The point moves 5 places left: \(4.5\times 10^{5}\).

Scoring: 1 point for each; award 0 if the coefficient is not between 1 and 10.

Question 2: Small numbers (2 points)

1. The point moves 6 places right: \(6.2\times 10^{-6}\).
2. The point moves 2 places right: \(7.05\times 10^{-2}\).

Scoring: 1 point for each; the sign of the exponent must be correct.

Question 3: Standard form (2 points)

1. Move the point 6 places right: 4,700,000.
2. Move the point 4 places left: 0.000309.

Scoring: 1 point for each correct number.

Question 4: Calculator display (2 points)

1. 6.4E-3 means \(6.4\times 10^{-3}\).
2. Move the point 3 places left: 0.0064.

Scoring: 1 point for each part.

Question 5: How many times as large (2 points)

1. \(\frac{8\times 10^{6}}{4\times 10^{2}}=\frac{8}{4}\times 10^{6-2}=2\times 10^{4}\), so the first is 20,000 times as large.

Scoring: 1 point for the quotient setup or coefficient 2, 1 point for the exponent 4 and the answer in scientific notation.

Question 6: Multiply and divide (2 points)

1. \(6\cdot3=18\) and \(4+(-7)=-3\), so \(18\times 10^{-3}=1.8\times 10^{-2}\).
2. \(9.6: 1.2=8\) and \(8-3=5\), so \(8\times 10^{5}\).

Scoring: 1 point for each; in part (a) the coefficient must be fixed to 1.8.

Question 7: Order and add (2 points)

1. The exponents are \(-4\), \(-3\), \(-5\). Order: \(8.9\times 10^{-5},\ 3.2\times 10^{-4},\ 1.5\times 10^{-3}\).
2. \(2.6+7.4=10\), so the sum is \(10\times 10^{5}=1\times 10^{6}\).

Scoring: 1 point for the correct order; 1 point for the sum written with coefficient 1.

Question 8: Phone storage (3 points)

1. Divide storage by video size: \(\frac{1.28\times 10^{11}}{8\times 10^{8}}\).
2. \(1.28: 8=0.16\) and \(11-8=3\), so \(0.16\times 10^{3}=1.6\times 10^{2}\).
3. \(1.6\times 10^{2}\) is 160 videos.

Scoring: 1 point for each part.

Question 9: Trip to the Sun (3 points)

1. \(\frac{9.3\times 10^{7}}{3\times 10^{4}}=3.1\times 10^{3}\) hours.
2. 3,100 hours \(: 24\approx129.2\), so about 129 days.
3. \(9.3\times 10^{7}\cdot5280=49.104\times 10^{10}\), which is \(4.9104\times 10^{11}\) feet.

Scoring: 1 point for each part; in part (c) the coefficient must be fixed to 4.9104.

⬇ Download the Grade 8 Scientific Notation test answer key (PDF, 111 KB)

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