Basic Math and Pre-Algebra

PART 1. The World of Numbers

CHAPTER 1. Our Number System

Rounding

When dealing with large quantities, sometimes you don’t need to use exact numbers. If you want to talk about a number being “about” or “approximately,” you want to round the number. For example, the number 6,492,391 is closer to 6 million than to 7 million, but closer to 6,500,000 than to 6,400,00. Rounding is a process of finding a number with the desired number of significant digits that is closest to the actual number.

DEFINITION

The significant digits of a number are the nonzero digits and any zeros that serve to tell you the precision of the measurement or the digit to which the number was rounded.

When you round a number, you place it between two other numbers and decide to which it is closer. To round 48,371 to the nearest ten-thousand, you need to decide if it’s closer to 40,000 or to 50,000. Any number from 40,001 up to 44,999 would be closer to 40,000, but numbers from 45,001 to 49,999 are closer to 50,000. The general agreement is that 45,000, right in the middle, will round to 50,000.

Because that middle number is the dividing line between the numbers that round down and those that round up, the digit after the last significant digit will tell you which way to round. If you want to round 48,371 to the nearest thousand, look to the hundreds place. The digit in that place is 3, so round down to 48,000. If you want to round it to the nearest hundred, the 7 in the tens place tells you to round up to 48,400.

To round a number:

1. Decide how many significant digits you want to keep.

2. Look at the next digit to the right.

3. If that digit is less than 5, keep the significant digits as they are and change the rest of the digits to zeros.

4. If that digit is 5 or more, increase the last significant digit by one and change the following digits to zeros.

Don’t worry if you start to round up and feel like you’ve started a chain reaction. If you round 99,999 to the nearest hundred, you’re placing 99,999 between 99,900 and the number 100 higher, which is 100,000. You see the 9 in the tens place and know you need to round up. That means you need to change the 9 in the hundreds place to a 10, and that doesn’t fit in one digit. That extra digit is carried over to the thousands place, which makes that a 10, and that carries over to the ten-thousands place. Take a moment to think about what numbers you’re choosing between, and you’ll know you’re in the right place.

CHECK POINT

Round each number to the specified place.

21. 942 to the nearest hundred

22. 29,348 to the nearest ten-thousand

23. 1,725,854 to the nearest hundred-thousand

24. 1,725,854 to the nearest thousand

25. 1,725,854 to the nearest million

The Least You Need to Know

• Our number system is a place value system based on powers of ten.

• As you move to the left, the value of each place is multiplied by 10.

• An exponent is a small number written to the upper right of a base number. The exponent tells you how many of the base number to multiply together.

• Scientific notation is a system of writing large numbers as a number between 1 and 10 multiplied by a power of 10.

• Round a number to a certain place by looking at the next place, rounding up if the next digit is 5 or more and down it’s 4 of less.