Answer Keys: Scientific Notation

Student Concept Worksheet Answers

1

7.5 x 10^9

7,500,000,000: Move decimal 9 places left. Coefficient is 7.5, exponent is 9.

2

8.2 x 10^-7

0.00000082: Move decimal 7 places right to get 8.2. Since original is small, exponent is -7.

3

1.2 x 10^9

(4 x 10^3) x (3 x 10^5) = 12 x 10^8 = 1.2 x 10^9. Multiply coefficients (4 x 3 = 12), add exponents (3 + 5 = 8), then adjust 12 to 1.2 and add 1 to exponent.

4

3.4 x 10^9 is larger

Compare exponents first: 10^9 > 10^8. Even though 9.1 > 3.4, the exponent 9 beats 8.

Practice Worksheet Answers

Part A: Converting to Scientific Notation

#	Answer	Explanation
1	4.5 x 10^7	45,000,000: Move decimal 7 places left
2	2.3 x 10^-5	0.000023: Move decimal 5 places right
3	6.7 x 10^9	6,700,000,000: Move decimal 9 places left
4	9.1 x 10^-7	0.00000091: Move decimal 7 places right
5	3.28 x 10^5	328,000: Move decimal 5 places left
6	5.2 x 10^-3	0.0052: Move decimal 3 places right

Part B: Converting to Standard Form

#	Answer	Explanation
7	380,000	3.8 x 10^5: Move decimal 5 places right
8	0.00072	7.2 x 10^-4: Move decimal 4 places left
9	90,500,000	9.05 x 10^7: Move decimal 7 places right
10	0.0000046	4.6 x 10^-6: Move decimal 6 places left

Part C: Multiplication and Division

11

8 x 10^8

(4 x 10^5) x (2 x 10^3) = (4 x 2) x 10^(5+3) = 8 x 10^8

12

3 x 10^4

(9 x 10^8) / (3 x 10^4) = (9/3) x 10^(8-4) = 3 x 10^4

13

3 x 10^8

(5 x 10^3) x (6 x 10^4) = 30 x 10^7 = 3 x 10^8 (adjust coefficient)

14

4 x 10^6

(8.4 x 10^9) / (2.1 x 10^3) = (8.4/2.1) x 10^(9-3) = 4 x 10^6

Part D: Comparing Numbers

#	Answer	Explanation
15	<	5.2 x 10^6 < 3.8 x 10^7 (exponent 6 < 7)
16	>	9.1 x 10^-4 > 8.5 x 10^-4 (same exponent, compare coefficients: 9.1 > 8.5)
17	>	7.3 x 10^5 > 7.3 x 10^4 (exponent 5 > 4)
18	>	2.5 x 10^-3 > 4.1 x 10^-5 (exponent -3 > -5, less negative means larger)

Part E: Word Problems

19

9.3 x 10^7 miles

93,000,000 = 9.3 x 10^7

20

7 x 10^-6 meters

0.000007 = 7 x 10^-6

21

1.5 x 10^11 meters

(3 x 10^8) x (5 x 10^2) = 15 x 10^10 = 1.5 x 10^11 meters

22

1.68 x 10^16 calculations

(8.4 x 10^12) x (2 x 10^3) = 16.8 x 10^15 = 1.68 x 10^16

Challenge Questions:

#23: (5.97 x 10^24) / (7.35 x 10^22) = (5.97/7.35) x 10^(24-22) = 0.812 x 10^2 = 8.12 x 10^1 = approximately 81 times. Earth is about 81 times more massive than the Moon.

#24: 1 x 2^18 = 262,144 = 2.62144 x 10^5 cells. After 6 hours (18 doubling periods), there would be approximately 2.62 x 10^5 bacteria cells.

FAST Practice Quiz Answers

1

B) 3.25 x 10^5

Only B has a coefficient between 1 and 10. A has 32.5 (too big), C has 0.325 (too small), D has 325 (way too big).

2

B) 4.72 x 10^-6

0.00000472: Move decimal 6 places right to get 4.72. Small number = negative exponent.

3

B) 2.4 x 10^9

(6 x 4) = 24, exponents: 5 + 3 = 8. So 24 x 10^8 = 2.4 x 10^9 (adjust coefficient to be between 1 and 10).

4

Select: 5.6 x 10^6, 56 x 10^5, 0.56 x 10^7, 560 x 10^4

All equal 5,600,000 except 5.6 x 10^5 = 560,000 (wrong!)
5.6 x 10^6 = 5,600,000 (correct, proper form)
56 x 10^5 = 5,600,000 (correct but not proper form)
0.56 x 10^7 = 5,600,000 (correct but not proper form)
5.6 x 10^5 = 560,000 (INCORRECT)
560 x 10^4 = 5,600,000 (correct but not proper form)

5

C) 8.5 x 10^8

Compare exponents first. 10^8 is largest exponent. Between A (10^7), B (10^8), C (10^8), D (10^6): B and C both have 10^8, but 8.5 > 1.2, so C is largest.

6

A) 1.28 x 10^4 km/hr

Speed = Distance / Time = (3.84 x 10^5) / (3 x 10^1) = (3.84/3) x 10^(5-1) = 1.28 x 10^4 km/hr

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