Name LESSON Date Class Reading Strategies 1-4 Follow a Procedure When you have an exponent with a base of 10, the number is called a power of 10. You can use some simple rules to find products with powers of 10. 13 103 32.5 103 13 (10 10 10) 32.5 (10 10 10) 13 1,000 32.5 1,000 Move the decimal point 3 places to the right. You need to add 3 zeros. 32,500. Move the decimal point 3 places to the right. You need to add 2 zeros. You can use powers of 10 to write large numbers in scientific notation. Scientific notation is used as a shortcut to write very large or very small numbers. To write 268,000,000 in scientific notation: Step 1: Move the decimal point to create a number between 1 and 10. Step 2: The number of places the decimal point is moved is the value of the exponent. 2.6.8.0.0.0.0.0.0. 2.68 108 Move the decimal point 8 places. So, the exponent is 8. 268,000,000 written in scientific notation is 2.68 108. Use 2.8 105 to answer Exercises 1–4. 1. How many times is 10 a factor? 2. Rewrite the number with 10 as a repeated factor. 3. How many places will you move the decimal point? How many zeros will be in the product? 4. What is the product of 2.8 x 105? Copyright © by Holt, Rinehart and Winston. All rights reserved. 33 Holt Mathematics Problem Solving 1-4 Applying Exponents Challenge 1-4 Computer Bytes LESSON LESSON Write the correct answer. Each byte in a computer’s memory represents about one character. The major units of computer memory are kilobytes (KB), megabytes (MB), and gigabytes (GB). 1 kilobyte 1,000 bytes 1 megabyte 1,000 kilobytes 1 gigabyte 1. Earth is about 150,000,000 kilometers from the sun. Write this distance in scientific notation. 1 KB 1,000 bytes 1.5 108 km 1 MB 1,000 KB 1,000 megabytes 1 GB 1,000 MB Write your answers using scientific notation. 1. In 1984, many personal computers had 64 KB of active (RAM) memory. How many bytes does this represent? 2. In 1992, many personal computers had 40 MB of hard drive memory. How many bytes does this represent? 4 6.4 10 bytes $7,600,000,000,000; 9 11 1 10 bytes 2.5 10 bytes Ming saved his computer files on floppy disks. Each disk holds up to 1.44 MB of memory. He used these disks to transfer his files to another computer. 5. How many bytes could each floppy disk hold? 6. Ming’s new computer has 120 GB of memory. How many disks could he transfer if each disk held 1.2 MB? 1.44 106 bytes 100,000 disks Rachel decided to back up her hard drive’s computer files by copying them onto compact disks (CDs). Each CD can hold up to 650 MB of memory, but Rachel saves only 600 MB on each. 7. How many bytes could each CD potentially hold? 8. If Rachel backs up 6 GB of memory, how many bytes of memory will she need? 6.5 108 bytes Choose the letter for the best answer. 5. China’s population in 2001 was approximately 1,273,000,000. Mexico’s population for the same year was about 1.02 108. How much greater was China’s population than Mexico’s? A 1,375,000,000 B 1,274,020,000 C 1,171,000,000 D 102,000,000 6. In mid-2001, the world population was approximately 6.137 109. By 2050, the population is projected to be 9.036 109. By how much will world population increase? F 151,730,000 G 289,900,000 H 1,517,300,000 J 2,899,000,000 7. The Alpha Centauri star system is about 4.3 light-years from Earth. One light-year, the distance light travels in 1 year, is about 6 trillion miles. About how many miles away from Earth is Alpha Centauri? A 2.58 1013 miles 8. In the fall of 2001, students in Columbia, South Carolina, raised $440,000 to buy a new fire truck for New York City. If the money had been collected in pennies, how many pennies would that have been? F 4.4 106 G 4.4 105 H 4.4 107 B 6 1013 miles C 1.03 1012 miles D 2.58 109 miles 6 109 bytes 31 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics Canada 7.6 1012 4 10 bytes 4. By 2005, many personal computers had 250 GB of hard drive memory. How many bytes does this represent? 4,500,000,000 km 4. Canada is about 1.0 107 square kilometers in size. Brazil is about 8,500,000 square kilometers in size. Which country has a greater area? 3. At the end of 2004, the U.S. federal debt was about $7 trillion, 600 billion. Write the amount of the debt in standard form and in scientific notation. 7 3. In 1997, many personal computers had 1 GB of hard drive memory. How many bytes does this represent? 2. The planet Neptune is about 4.5 109 kilometers from the sun. Write this distance in standard form. J 4.4 3 108 32 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics Puzzles, Twisters & Teasers 1-4 Oh, the Power of Tens! Reading Strategies 1-4 Follow a Procedure LESSON LESSON Substitute the correct number for the letter or letters in each equation. Use your answers to solve the riddle. When you have an exponent with a base of 10, the number is called a power of 10. You can use some simple rules to find products with powers of 10. 13 103 32.5 103 13 (10 10 10) 32.5 (10 10 10) 13 1,000 32.5 1,000 4 P 5 2. 280,000 2.8 10 3. 592,000 I 105 5.92 4. 16,800 C 104 1.68 A Move the decimal point 3 places to the right. You need to add 3 zeros. 8 5. 5.4 10H 540,000,000 32,500. 1. 24,500 2.45 10E 6. 24,400,000 S 10 Move the decimal point 3 places to the right. You need to add 2 zeros. 2.44; 7 What’s a Martian’s favorite snack? You can use powers of 10 to write large numbers in scientific notation. Scientific notation is used as a shortcut to write very large or very small numbers. S P A C E C H I P S 2.44 5 7 1.68 4 1.68 8 5.92 5 2.44 To write 268,000,000 in scientific notation: Step 1: Move the decimal point to create a number between 1 and 10. Step 2: The number of places the decimal point is moved is the value of the exponent. Move the decimal point 8 places. 2.6.8.0.0.0.0.0.0. 2.68 108 So, the exponent is 8. 268,000,000 written in scientific notation is 2.68 108. Use 2.8 105 to answer Exercises 1–4. 5 times 1. How many times is 10 a factor? 2. Rewrite the number with 10 as a repeated factor. 2.8 10 10 10 10 10 3. How many places will you move the decimal point? How many zeros will be in the product? Copyright © by Holt, Rinehart and Winston. All rights reserved. 5 places; 4 280,000 4. What is the product of 2.8 x 105? 33 Copyright © by Holt, Rinehart and Winston. All rights reserved. Holt Mathematics Copyright © by Holt, Rinehart and Winston. All rights reserved. 106 34 Holt Mathematics Holt Mathematics