Numbers and Computation

Transcription

1 hot topics Numbers and Computation Place Value of Whole Numbers 70 Properties 74 Order of Operations 78 Factors and Multiples 80 Integer Operations 88

2 What do you already know? You can use the problems and list of words below to see what you already know about this chapter.the answers to the problems are in Hot Solutions at the back of the book, and the definitions of the words are in Hot Words at the front of the book.you can find out more about a particular problem or word by referring to the boldfaced topic number (for example, 1 2). Problem Set Give the value of the 3 in each number ,514 30, ,154,987 30,000,000 (2 10,000) (4 1,000) (3 100) 3. Write 24,378 using expanded notation. 1 1 (7 10) (8 1) 4. Write in order from greatest to least: 56,418; 566,418; 5,618; 496, ,418; 496,418; 56,418; 5, Round 52,564,764 to the nearest ten, thousand, and million ,564,760; 52,565,000; 53,000,000 Solve (5 3) , , Solve. Use mental math if you can (31 69) ,600 Use parentheses to make each expression true (4 6) (10 14) (3 3) 4 Is it a prime number? Write Yes or No No No No Yes Write the prime factorization for each Find the GCF for each pair and and and Find the LCM for each pair and and and 40 80

3 Numbers and Computation What is the least common multiple of 2, 3, and 16? Give the absolute value of the integer. Then write its opposite , , , , 25 Add or subtract ( 3) ( 9) ( 3) ( 8) Compute ( 7) ( 12) ( 6) ( 4 3) ( 3) [ 6 ( 4)] [5 ( 7)] What can you say about the product of a negative integer and a positive integer? 1 5 It will be a negative integer. 45. What can you say about the sum of two positive integers? 1 5 It will be a positive integer. WHAT DO YOU KNOW? hot words absolute value 1 5 approximation 1 1 associative property 1 2 common factor 1 4 commutative property 1 2 composite number 1 4 distributive property 1 2 expanded notation 1 1 factor 1 4 greatest common factor 1 4 CHAPTER 1 least common multiple 1 4 multiple 1 4 negative integer 1 5 negative number 1 5 number system 1 1 operation 1 3 PEMDAS 1 3 place value 1 1 positive integer 1 5 prime factorization 1 4 prime number 1 4 round 1 1

4 70 Hot Topics 1 1 PLACE VALUE 1 1 Place Value of Whole Numbers Understanding Our Number System You know that our number system is based on 10 and that the value of each place is 10 times the value of the place to its right. The value of a digit is the product of that digit and its place value. For instance, in the number 5,700, the 5 has a value of five thousands and the 7 has a value of seven hundreds. A place-value chart can help you read numbers. In the chart, each group of three digits is called a period. Commas separate the periods. The chart below shows the area of Asia, the largest continent. The area is about 17,300,000 square miles. That is nearly twice the size of North America. TRILLIONS BILLIONS MILLIONS THOUSANDS ONES Hundred Trillions Ten Trillions One Trillions Hundred Billions Ten Billions One Billions Hundred Millions Ten Millions One Millions Hundred Thousands,, 7, 3 0, To read a large number, think of the periods. At each comma, say the name of the period. 17,300,000 reads: seventeen million three hundred thousand. Give the value of the 3 in each number , ,000,297 3,000,000 Write each number in words ,306, ,030,500,000,000 One Thousands Hundreds Ten Thousands Tens Ones Forty million, three-hundred-six thousand, two hundred 4. Fourteen trillion, thirty billion, five-hundred million

5 Numbers and Computation 71 Using Expanded Notation To show the place values of the digits in a number, you can write the number using expanded notation. You can write 50,203 using expanded notation. 50,203 50, Write the ten thousands. (5 10,000) Write the thousands. (0 1,000) Write the hundreds. (2 100) Write the tens. (0 10) Write the ones. (3 1) So 50,203 (5 10,000) (2 100) (3 1). Use expanded notation to write each number , , (8 10,000) (3 1,000) (4 10) (6 1) 6. (3 100,000) (2 100) (8 10) (5 1) Comparing and Ordering Numbers When you compare numbers, there are exactly three possibilities: the first number is greater than the second (2 1); the second is greater than the first (3 4); or the two numbers are equal (6 6). When ordering several numbers, compare the numbers two at a time. 1 1 PLACE VALUE COMPARING NUMBERS Compare 35,394 and 32,915. Line up the digits, starting with the ones. 35,394 32,915 Beginning at the left, look at the digits in order. Find the first place where they differ. The digits in the thousands place differ. The number with the greater digit is the greater So 35,394 is greater than 32,915.

6 72 Hot Topics 1 1 PLACE VALUE Write,,or , , ,004 51,888 Write in order from least to greatest ,302; 52,617; 6,520; 526,000 6,520; 52,617; 56,302; 526,000 Using Approximations For many situations, using an approximation makes sense. For instance, it is reasonable to use a rounded number to express population. You might say that the population of a place is about 60,000 rather than saying it s 58,889. Use this rule to round numbers. Look at the digit to the right of the place to which you are rounding. If the digit is 5 or greater, round up. If it is less than 5, round down. Round 123,456 to the nearest hundred. Hundreds 123, So 123,456 rounds to 123, Round 32,438 to the nearest hundred. 32, Round 558,925 to the nearest ten thousand. 560, Round 2,479,500 to the nearest million. 2,000, Round 369,635 to the nearest hundred thousand. 400,000

7 Numbers and Computation EXERCISES Give the value of the 4 in each number , , ,014,257 4,000 Write each number in words ,607,400 Twenty-two million, six-hundred-seven thousand, four hundred 4. 3,040,680,000,000 Three trillion, forty billion, six-hundred-eighty million Use expanded notation to write each number ,056 (4 10,000) (6 1,000) (5 10) (6 1) 6. 4,800,325 (4 1,000,000) (8 100,000) (3 100) (2 10) (5 1) Write,,or , , ,106 58,995 Write in order from least to greatest ,388; 83,725; 18,652; 380,735 18,652; 38,388; 83,725; 380,735 Round 48,463,522 to each place indicated. 10. nearest ten 48,463, nearest thousand 48,464, nearest hundred thousand 48,500, nearest ten million 50,000,000 Solve. 14. In the first year, a video game had total sales of $226,520,000. During the second year, sales were $239,195,200. Did the game earn more money or less money in the second year? How do you know? More money; greater digit in the ten millions place 15. About 2,000,000 people visited the aquarium last year. If this number was rounded to the nearest million, what was the greatest number of visitors? What was the least number? 2,499,999; 1,500, EXERCISES