1. Express the number 80,000 in scientific notation.
2. Express the number 60,000 in scientific notation.
3. Think About the Process You want to express 437,000 in scientific notation.
a. What is the first step?
A. Move the decimal point 5 places to the left to get 4.37.
B. Move the decimal point 4 places to the left to get 4.37.
C. Move the decimal point 4 places to the left to get 43.7.
D. Move the decimal point 5 places to the left to get 43.7.
b. What is the result?
4. Express the number 8.5 × 105 in standard form.
5. The diameter of a certain star is about 9.3 × 106 km. Express this diameter in standard form.
6. Express 0.006 in scientific notation by counting decimal places.
7. Mental Math Express this number in scientific notation.
a. Writing Express the number 5.2 × 106 in standard form.
b. Describe two advantages that scientific notation has over standard form. Describe two advantages of standard form. Give examples for each.
a. Writing Express 0.00000843 in scientific notation.
b. How can negative powers of 10 make small numbers easier to write and compare?
10. Write 0.0000000485 in scientific notation by counting decimal places.
11. Error Analysis Owen incorrectly claims that because 20,000 = 20 × 1,000, he can express 20,000 in scientific notation as 20 × 103.
a. What was Owen's error?
A. The product he found is correct, but 20 × 103 is not in scientific notation since 20 is not less than 10.
B. The product he found is correct, but 20 × 103 is not in scientific notation since 20 is not less than 1.
C. He found the power of 10 incorrectly since 1,000 ≠ 103.
D. He found the product incorrectly since 20,000 ≠ 20 × 1,000.
b. Express 20,000 in scientific notation correctly.
12. Population A historian predicts that by 2050, about 1.56 × 107 people will live in a certain country. Express this prediction in standard form.
a. Express the number 586,400,000 in scientific notation.
b. Describe a situation in which this number might arise. Explain why it would be easier to use scientific notation in that situation.
14. A nanometer is one-billionth of a meter. A centimeter is one-hundredth of a meter, and a kilometer is 1,000 meters. An X-ray can have a wavelength of 0.000000037 meter.
a. Express this wavelength in scientific notation.
b. Which unit is most appropriate for measuring the wavelength of an X-ray? Explain your reasoning.