Review the following concepts if needed:

- Subscripts and Superscripts Help
- Power of Ten Help
- Rules for Use of Power of 10 Notation Help
- Approximation, Error, and Precedence Help
- Significant Figures Help

**Scientific Notation Practice Test**

A good score is eight correct.

1. What is the sine of 30° 0′ 0″ to three significant figures?

(a) 0.5

(b) 0.50

(c) 0.500

(d) 0.5000

2. Using a calculator, find the tangent of (90 – 0.00035675)° and round it off to three significant figures in the most unambiguous way possible.

(a) 161,000

(b) 160,605

(c) 1.606 × 10 ^{5}

(d) 1.61 × 10 ^{5}

3. Suppose the angular diameter of a distant galaxy is measured, and is found to be 0° 30′ 0″ ± 10%. The error can vary up to plus or minus:

(a) 5°

(b) 0.5°

(c) 0.05°

(d) 0.005°

4. What is the value of 2 × 4 ^{2} - 6?

(a) 26

(b) 58

(c) 20

(d) There is no way to tell because it is an ambiguous expression

5. Two numbers differ in size by exactly six orders of magnitude. This is a factor of:

(a) 6

(b) 6 × 10

(c) 10 × 10 × 10 × 10 × 10 × 10

(d) 2 ^{6}

6. Suppose we invent a new unit of angular measure called the flummox (symbol: Fx). We can call 1.00 × 10 ^{–9} flummox

(a) one milliflummox (1.00 mFx)

(b) one nanoflummox (1.00 nFx)

(c) one picoflummox (1.00 pFx)

(d) one kiloflummox (1.00 kFx)

7. What is the value of sin ^{3} (1), assuming the angle represents precisely one radian, truncated (not rounded off) to three significant figures?

(a) 0.596

(b) 0.595

(c) 8.415 × 10 ^{–1}

(d) 0.841

8. What is the order in which operations should be performed in an expression containing no parentheses?

(a) Addition, then subtraction, then multiplication, then division, and finally exponentiation

(b) Exponentiation, then multiplication and division, and finally addition and subtraction

(c) From left to right

(d) From the inside out

9. Which of the following expressions might indicate the direction angles of a vector in three-space?

(a) *β* _{1} , *β* _{2} , *β* _{3}

(b) ( *θ* ^{1} , *θ* ^{2} , *θ* ^{3} )

(c) (1 _{θ} ,2 _{θ} ,3 _{θ} )

(d) Any of the above

10. What is the product of 8.72 × 10 ^{5} and 6.554 × 10 ^{–5} , taking significant figures into account?

(a) 57.15088

(b) 57.151

(c) 57.15

(d) 57.2

**Answers:**

1. c

2. d

3. c

4. a

5. c

6. b

7. b

8. b

9. a

10. d

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