Scientific Notation Test Answer Key with Scoring – Grade 8

Question 1 Write in scientific notation (3 points)

1. Left 7 places: 7.2 × 10⁷.
2. Right 6 places: 4.6 × 10⁻⁶.
3. Left 5 places: 9.03 × 10⁵.

(a) 7.2 × 10⁷ (b) 4.6 × 10⁻⁶ (c) 9.03 × 10⁵

Scoring: 1 point per part.

Question 2 Standard form (2 points)

1. Three places left: 0.00507.
2. Six places right: 1,800,000.

(a) 0.00507 (b) 1,800,000

Scoring: 1 point per part.

Question 3 Products and quotients (3 points)

1. 6 · 5 = 30 and 4 + 3 = 7, so 30 × 10⁷ = 3 × 10⁸.
2. 7.2 ÷ 9 = 0.8 and 8 − 3 = 5, so 0.8 × 10⁵ = 8 × 10⁴.

(a) 3 × 10⁸ (b) 8 × 10⁴

Scoring: (a) 1 point for 30 × 10⁷, 1 point for normalizing. (b) 1 point.

Question 4 Order by size (2 points)

In decimals: 0.00025, 0.00009, 0.0013, 0.0006. Compare exponents: −5 is the smallest, then −4 (2.5 < 6), then −3.

9 × 10⁻⁵, 2.5 × 10⁻⁴, 6 × 10⁻⁴, 1.3 × 10⁻³

Scoring: 2 points for the correct order, 1 point if only one pair is swapped.

Question 5 Two reservoirs (3 points)

1. (2 × 10⁷) ÷ (4 × 10⁶).
2. 2 ÷ 4 = 0.5 and 7 − 6 = 1, so 0.5 × 10¹ = 5.
3. Reservoir B holds 5 times as much.

(a) (2 × 10⁷) ÷ (4 × 10⁶) (b) 5 (c) 5 times

Scoring: 1 point per part.

Question 6 Addition and calculators (3 points)

(a) 4.5 × 10⁴ = 0.45 × 10⁵. Then 8.1 + 0.45 = 8.55, giving 8.55 × 10⁵.

(b) 6.4E−5 means 6.4 × 10⁻⁵ = 0.000064.

(a) 8.55 × 10⁵ (b) 0.000064

Scoring: (a) 1 point for matching exponents, 1 point for the sum. (b) 1 point.

Question 7 Pollen grain (2 points)

2.5 × 10⁻⁵ m = 25 × 10⁻⁶ m = 25 micrometers. In millimeters it would be 0.025, and in meters 0.000025, so micrometers give the simplest number.

25 micrometers

Scoring: 1 point for the unit, 1 point for 25.

Question 8 Decimal point journey (2 points)

The point moves 4 places to the right, giving coefficient 9.3. Since the original number is less than 1, the exponent is negative: 9.3 × 10⁻⁴.

9.3 × 10⁻⁴

Scoring: 1 point for the number, 1 point for the explanation.