Bell Work:Helen has a 4-kilometer head start on Paris. How long will it take Paris to catch Helen if Helen travels at 6 kilometers per hour and Paris travels at 8 kilometers per hour?

Answer:D + 4 = DR T + 4 = R TR = 6R = 8T = T2 hours

H P

H H P P

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Lesson 100:Place Value, Rounding Numbers

In this book we have rounded most answers to a few decimal places and have not extensively practiced the skill of rounding numbers. In this lesson we will review the process of rounding to any designated number of digits. Future problem sets will provide problems that allow us to practice rounding.

We use the 10 digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

To write the decimal numerals that we use to represent numbers. The value of a digit in a numeral depends on the position of the digit with respect to the decimal point.

For instance, in the numeral40,632,903.195034

The first 9 has a value of 900 because it is in the hundreds’ place, three places to the left of the decimal point. The second 9 has a value of only 9/100 because it is written in the hundredths’ place, which is two places to the right of the decimal point.

It is important to note that the first place to the right of the decimal point is the tenths’ place, whereas the tens’ place is not one place but two places to the left of the decimal point. The first place to the left of the decimal point is the units’ (or ones’) place.

Often we use numbers that are approximations of other numbers. For instance, the circumference of the earth at the equator is 24,874 miles. This measurement is to the nearest mile and is a difficult number to remember. So we say that circumference is 25,000 miles and say that we have rounded to the nearest thousand. This is because 24,874 is closer to 25,000 than it is to 24,000. thus, when we round, we change the digits at the end of the number to zeros.

Rounding requires three steps, and mistakes can be avoided if a circle and an arrow are used as aids. To demonstrate, we will round 24,874 to the nearest thousand.

1. Circle the digit in the place to which we are rounding and mark the digit to its right with an arrow.

2 4 8 7 4

2. Change the arrow marked digit and all digits to it right to zero

2 4 0 0 0

3. Leave the circled digits unchanged or increase 1 unit as determined by the following rules:a) If the arrow marked digit was originally less than 5, do

not change the circled digit.b) If the arrow marked digit was originally greater than 5 or

is a 5 followed somewhere by a nonzero digit, increase the circled digit by 1 unit. This rule applies to the problem we are working, so we finish by writing 25,000

c) If the arrow marked digit was originally a terminal 5 or a 5 followed only by zeros, the number is hallway between the two possible numbers for the rounded answer; the circled digit can be left unchanged or can be increased by 1 as you wish. The procedure to be used in this case is really not important, and we will try to avoid this case in the problem sets. Concentrate on rules a and b.

Example:Round 47,258,312.065 to the nearest ten thousand.

Answer:47,260,000

Example: Round 104.06245327 to the nearest thousandths.

Answer:104.062

Example:Round 0.00041378546 to the nearest one-hundred-millionth

Answer:0.00041379

Example:Round 2.0031664567 to five decimal places.

Answer:2.00317

HW: Lesson 100 #1-30