LH8a
Practice - Scientific Notation
TRY TO ANSWER IN TWO AND A HALF MINUTES.
QUESTIONS
QUESTIONS
1. Nanotechnology deals with technology at the molecular scale. The prefix nano means one-billionth, and a nanometer is 10⁹ meter. To give another perspective, a nanometer of of the order of 1/10⁵ times the width of a human hair or, said another way, a human hair is about 90,000 nanometers wide. Write this number in scientific notation.
2. The U.S. population is 3.5 x 10⁸ and the total population of North America is 5.2 x 10⁸. The U.S. population is (greater than, equal to, or less than) the population of the other countries in North America?
3. In scientific notation, what is the exponent of (4.8 x 10⁶) times (3.2 x (1/10⁴))?
4. According to some estimates, the earth is 4,540,000,000 years old. Put this number into scientific notation.
5. Convert the following numbers from scientific notation to standard notation: 3.7 x 10⁶ , 8.591 x 10⁷ , 7.2 x 10 -³ , 4.8 x 10⁸ .
6. A mile has 5,280 feet. How much is this in scientific notation?
ANSWERS
1. 90,000 = 9 x 10⁴. Notice that most of the question is not relevant to the answer.
2. The population the other countries equals the North American population minus the U.S. population. You can do this subtraction directly because both numbers are expressed with 10⁸. The difference is 5.2 - 3.5 = 1.7 x 10⁸. The U.S. population (3.5 etc.) is greater than the population of the rest of North America (1.7 etc.)
3. First subtract the powers, which is 6 - 4 = 2. But then recognize that the product would be 15.36, which in scientific notation would be converted to 1.536 x 10¹ . So the answer is 3, which is the difference of 2, plus 1. With the built-in calculator you could do this directly and perhaps more easily.
4. 4.54 x 10⁹ . The decimal point moves 9 places to the left, which makes the exponent of 10 equal to 9.
5. In order, 3,700,000. 85,9100,000. 0.0072. 480,000,000.
6. 5.28 x 10³ .