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This table explains the prefixes kilo, mega, and giga.
4. a. Calculate how many bytes are in one kilobyte. Estimate your answer using a power of ten.
b. How many bytes are in one megabyte? Write your answer in scientific notation. Estimate your answer using a power of ten.
(You may want to use a calculator for this.)
c. How many kilobytes are in one megabyte? How do you know?
The relationship between kilobytes and megabytes holds true for megabytes and gigabytes. One gigabyte is more than 1,000 times one megabyte.
d. How many bytes are in one gigabyte? Write your answer as a power of two.
5. In problem 21 of Section E, you learned how to read a binary clock. Sketch a binary clock and color the lights so the time displayed is 3:12 P.M.
Additional Practice 59
Additional Practice
IT Terminology
one kilobyte 1 kB 210bytes one megabyte 1 mB 220bytes one gigabyte 1 gB ... bytes
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1. a. 1,000 10 10 100,000 b. 1,000 1,000 1,000,000 c. 63.7 10 637
d. 63.7 100 6,370 e. 0.58 1,000 580
2. a. Here are five sample products of one billion.
1,000 1,000,000 1,000 1,000 1,000
10 10 10 10 10 10 10 10 10 10 100,000,000
100 10,000,000
You might have others; check with a classmate to make sure the product is 1,000,000,000.
b. Here are five sample products for 2,270,000.
2,270 1,000 22.7 100,000 227 10,000 227 100 100 227 10 1,000
You might have others; check with a classmate to make sure the product is 2,270,000.
3. a. 107or 10,000,000, or ten million b. 1010or 10,000,000,000 or ten billion c. 106or 1,000,000 or one million
(10 100 1,000 101 102 103) d. 109or 1,000,000,000 or one billion
(1,000,000 10,000 106 104) (1,000 1,000,000 103 106)
4. a. 2.25104➞ 22.5103➞ 225102➞ 2,25010 ➞ 22,500 b. Check the work of the classmate who solved your problem.
Section A Base Ten
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5. a. Both calculators display 5.1 and 06; 5.1 is the first factor between 1 and 10; 06 is the exponent of 10. The difference is the second display uses an E to designate the exponent of ten;
the first one displays the exponent of ten as a small number in the upper right corner.
b. 5.1 106or 5.1 million or 5,100,000
1. Yes, groups of three work because the sum of the digits of 945 is 18: 9 4 5 18, and 18 is divisible by 3.
No, groups of six will not work. “Divisible by 6” means that the number 945 has to be divisible by 3 and by 2. Because 945 is not an even number, it is not divisible by 2, so it is not divisible by 6.
2. a. 1, 3, 5, and 15 b. 1, 2, 4, 8, 16, and 32 c. 1 and 53
d. 1 and 17
3. a. The number you wrote can be even or odd but must not be a perfect square number. One sample number that has an even number of factors is 20; the factors of 20 are 1, 2, 4, 5, 10, and 20.
b. The number you wrote must be any perfect square number.
Sample numbers with an odd number of factors are 25 or 100.
c. A perfect square number will always have an odd number of factors.
4. There are 10 perfect square numbers from 1 through 100: 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.
Answers to Check Your Work 61
Answers to Check Your Work
Section B Factors
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1. There are many ways to calculate with an arithmetic tree. In all cases, your final answer is 1,400.
Here are two different ways:
2. The numbers 12, 39, and 51 are all composite numbers.
Sample reasoning:
Prime numbers have exactly two factors, 1 and itself. Composite numbers are numbers larger than one that are not prime. One way to find out whether or not a number is a composite number is to use the rules for divisibility.
12 is an even number, so it is divisible by 2 and has more factors than 1 and 12.
19 1 19; 19 has no other factors than 1 and 19, so 19 is prime.
39 3 13, so 39 has more factors than 1 and 39.
51 is divisible by 3 because the sum of the digits is 6, and 6 is divisible by 3, so 51 has more factors than 1 and 51.
Answers to Check Your Work
Section C Prime Numbers
5 2
4
20
700
1,400 35
7 5
2 5
10
200 20
7 4 5
1,400
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3. a. 99 3 3 11 b. 750 2 3 5 5 5
c. 264 2 2 2 3 11
4. A strategy to solve these problems is to find all factors of the number of centimeter cubes first.
a. The factors of 8 are: 1, 2, 4, and 8.
Three possible dimensions are:
1 cm by 1 cm by 8 cm, 1 cm by 2 cm by 4 cm, and 2 cm by 2 cm by 2 cm.
b. The factors of 50 are: 1, 2, 5, 10, 25, and 50.
Three possible dimensions are:
1 cm by 2 cm by 25 cm, 1 cm by 5 cm by 10 cm, and 2 cm by 5 cm by 5 cm.
Answers to Check Your Work 63
Answers to Check Your Work
2 5
10
5
5
3 25
75 99 9 11 750
(3 3) 11 3 3 11
264 132 66 33 11 1
2 2 2 3 11
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1. a. The base is 2.
b. The exponent is 5.
c. 25 2 2 2 2 2 32 2. a. The side length is 1200 ≈ 34.64 in.
b. The side length is 120 ≈ 10.95 in.
c. The side length is 12≈ 3.46 in.
d. The side length is 1.2 ≈ 1.095 in., or 1.10 in.
e. The side length is 0.12 ≈ 0.364 in., or 0.35 in.
f. If the area is 100 times as small, then the side length is ten times as small. Compare, for example, a and c or c and e.
Answers to Check Your Work
Section D Square and Unsquare
1 mile
1 square mile 1 mile one city block
1 mile12
3 mile
8
3. a. The area of one city block is ––1
64square mile.
Sample reasoning:
One city block is ––1
8 mile by ––1 8 mile.
In one square mile (see drawing), you can fit eight rows of eight city blocks. This makes 8 rows 8 blocks or 64 blocks.
If 64 city blocks fit in one square mile, then the area of one city block is ––1
64of a square mile.
b. ––3
8 1––12 –––3664, or ––9 16
Here is a way to calculate––3
8 1––12 using city blocks.
––3
8 mile is 3 city blocks.
1––1
2 miles are 12 city blocks (8 4).
––3
8 1––12 is the same as
3 blocks 12 blocks, or 36 blocks.
Since 1 city block is ––1
64square mile, 36 city blocks is –––36
64 square mile.
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4. 3 ––1
2 2 ––13 8 ––16
One sample strategy using the area model:
The four parts total 8 ––1
6, (6 1 1––16).
1. Many answers are possible. Here are three samples:
10,000 24 54 10,000 102 102 10,000 22 52 102
Make sure you use a product of powers; 10,000 104is one power and not a product of powers.
2. a. 288 2 2 2 2 2 3 3
25 32
b. 900 2 2 3 3 5 5
22 32 52
c. 1764 2 2 3 3 7 7
22 32 72 3. 23 52 2 2 2 5 5
200 4. a. 27 81 2,187
Explanation:
You can use the table to find 27 33and 81 34 27 81 33 34
37
In the table, 37 2,187.
Answers to Check Your Work 65
Answers to Check Your Work
Section E More Powers
2 13
3
1 2
6
1 16
1
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