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To finish the problem, you can divide 1,006 into 1,413 just 1 time. So this time, write 1 above the line after the 4, multiply
Therefore,
Unit 2
The Big Four Operations: Addition, Subtraction, Multiplication, and Division
In This Unit …
1 Chapter 3: Counting on Success: Numbers and Digits Knowing Your Place Value Close Enough for Rock ‘n’ Roll: Rounding and Estimating Practice Questions Answers and Explanations Whaddya Know? Chapter 3 Quiz Answers to Chapter 3 Quiz
2 Chapter 4: Staying Positive with Negative Numbers Understanding Where Negative Numbers Come From Sign-Switching: Understanding Negation and Absolute Value Addition and Subtraction with Negative Numbers Knowing Signs of the Times (and Division) for Negative Numbers Practice Questions Answers and Explanations Whaddya Know? Chapter 4 Quiz Answers to Chapter 4 Quiz
3 Chapter 5: Putting the Big Four Operations to Work Switching Things Up with Inverse Operations and the Commutative Property Getting with the In-Group: Parentheses and the Associative Property Understanding Inequalities Moving Beyond the Big Four: Exponents and Square Roots Practice Questions Answers and Explanations Whaddya Know? Chapter 5 Quiz Answers to Chapter 5 Quiz
Chapter 3
Counting on Success: Numbers and Digits
IN THIS CHAPTER
When you’re counting, ten seems to be a natural stopping point — a nice, round number. The fact that our ten fingers match up so nicely with numbers may seem like a happy accident. But of course, it’s no accident at all. Fingers were the first calculator that humans possessed. Our number system — the Hindu-Arabic numbers, also called the decimal numbers — is based on the number ten because humans have 10 fingers instead of 8 or 12. In fact, the very word digit has two meanings: numerical symbol and finger.
In this chapter, I show you how place value turns digits into numbers. I also show you when 0 is an important placeholder in a number and why leading zeros don’t change the value of a number. And I show you how to read and write long numbers. After that, I discuss two important skills: rounding numbers and estimating values.
TELLING THE DIFFERENCE BETWEEN NUMBERS AND DIGITS
Sometimes people confuse numbers and digits. For the record, here’s the difference:
A digit is a single numerical symbol, from 0 to 9.
A number is a string of one or more digits.
For example, 7 is both a digit and a number. In fact, it’s a one-digit number. However, 15 is a string of two digits, so it’s a number — a two-digit number. And 426 is a three-digit number. You get the idea.
In a sense, a digit is like a letter of the alphabet. By themselves, the uses of 26 letters, A through Z, are limited. (How much can you do with a single letter such as K or W?) Only when you begin using strings of letters as building blocks to spell words does the power of letters become apparent. Similarly, the ten digits, 0 through 9, have limited usefulness until you begin building strings of digits — that is, numbers.
Knowing Your Place Value
The number system you’re most familiar with — Hindu-Arabic numbers — has ten familiar digits:
Yet with only ten digits, you can express numbers as high as you care to go. In this section, I show you how it happens.
Counting to ten and beyond
The ten digits in our number system allow you to count from 0 to 9. All higher numbers are produced using place value. Place value assigns a digit a greater or lesser value, depending on where it appears in a number. Each place in a number is ten times greater than the place to its immediate right.
To understand how a whole number gets its value, suppose you write the number 45,019 all
