1.2+Rounding+Numbers

Section 1.2 - Rounding and Estimating Numbers
There are some elements of space travel that need to be very accurate and precise, and others that don't matter so much. Two millimeters off on a fuel coupling may destroy a spacecraft, but imagine the press conference where the public relations guy announces that the craft is expected to travel exactly 408,242.987 meters. Wouldn't it suffice to say "just over 400,000 meters"? Although not as accurate or as precise, it's easier on the mind to comprehend and remember.

Another use for rounding might be when you are estimating the number of sequins needed for making an 80's prom dress and they are sold only in packages of 100. Even a novice dressmaker should be able to decide if it is a 2200 sequin dress or 2300.

There are three slightly different ways to round numbers:
 * To a particular place
 * Front-end rounding
 * Always rounding up


 * Rounding to a Specific Place**

If a number is rounded to a particular place, such as the hundreds place, it is rounded __up or down__ to the nearest hundred. So, rounding 32,743 to the nearest hundred would produce 32,700 because it is closer to 32,700 than it is to 32,800.


 * Rounding Rules**

1. Underline the place to be rounded to. 2. Look at the digit to the right of this place. -- If it is 5 or higher, move the underlined digit up by 1. -- If it is less than 5, leave the underlined digit where it is. 3. Change all digits to the right of the underlined one to zeroes. 4. If the zeroes are on the right of the decimal point, just drop them.

In this example, we are rounding to the tens place: 1,497 Following the rules, we underline the 9. Because 7 is "5 or higher", the 9 would be raised to 10. Because 10 cannot fit in the tens spot, it is essentially "carried" as in double digit addition. 1,497 rounds to 1,500 as the nearest ten.


 * Rounding Negative Numbers**

The same rules apply when rounding a negative number. One way to look at it is to simply ignore the negative sign and round it according to the rules, then put the sign back in front. Rounding -2,134 to the nearest hundred would be -2,100.


 * Front-end Rounding**

Front-end rounding using the same rules for rounding to a specific place, but the number is always rounded to its highest place (furthest left). If you are asked to round a number, but not told the specific place value, use front-end rounding.


 * Application Problems**

Although rounding to the nearest hundred works fine for most problems, some real-life applications require you to modify the process slightly. An example would be buying juices for the soccer team. Suppose there are 13 kids on the team, but the juices come in packs of 6 boxes. Two packs (12) would certainly be closer than 3 packs (18), but in this case it makes sense to round up (although it might be easier to console the kid who doesn't get a juice than it is to decide who gets the extra ones.)


 * Estimating**

Estimating and rounding are related, but not the same. Estimating is essentially doing math with numbers that have been rounded first.

1. Round the numbers using front-end rounding. 2. Then do the math.

Examples:

See also: Rounding fractions

1.1 Place Value 1.2 Rounding and Estimating Numbers 1.3 Addition 1.4 Subtraction 1.5 Multiplication 1.6 Division 1.7 Exponents 1.8 Order of Operations 1.9 Prime Numbers
 * Where to from here?**
 * Chapter One Review**
 * Chapter One Homework**