PreAlgebra

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Chapter 5 Decimals

5-1 Naming Decimals

Decimal numbers, like fractions, allow us to express fractional parts of a number—including places between the integer values on the number line.

The example in Figure 4-1 shows how decimal numbers are located on the number line. One of the values is between -3 and -2, and the other is somewhere between +2 and +3.

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Figure 4-1. Decimal fractions as they appear on the standard number line.

There are three parts to a decimal number:

An integer
A decimal point
A decimal fraction

A decimal consists of an integer and a decimal fraction, separated by a decimal point.

Example

Here are the three parts of the decimal number, 2.14

Decimal fractions play the same roles in mathematics as the numerator-and-denominator fractions that you have already studied in these lessons. However, you will soon discover that decimal fractions are much more useful and far easier to work with.

Figure 4-2A shows the first seven place values for a typical whole-number value. You've seen this before: ones, tens, hundreds, thousands, ten-thousands, and so on. As shown in Figure 4-2B, A Decimal number has three parts, including a whole-number part. And, just as before, the whole-number part has place values called tens, hundreds, thousands, and so on. But the decimal fraction part is different.

(A)	(B)
Figure 4-2. Comparing place values for whole numbers (A) and decimal numbers (B).

In a decimal number, the decimal point is the starting point for determining place values. Place value on the left side of the decimal point are the whole-number values. Place values on the right side of the decimal point are the decimal-fraction place values.

Place values for the whole-number part of a decimal number begin with ones and increase in the left-hand direction.
Place values for the decimal fraction part of a decimal number begin with tenths and increase in the right-hand direction.

You can see that the names for the whole-number and decimal-fraction parts of a decimal number are very similar. See Table 4-1. Wheras whole-number place values are called tens, hundreds, thousands, and so on, decimal-fraction place values are called tenths, hundredths, thousandths, and so on.

Table 4-1. Names for the place values found in decimal fractions.

Whole-Number Part	Decimal-Fraction Part
tens	tenths
hundreds	hundredths
thousands	thousandths
ten-thousands	ten-thousandths
hundred-thousands	hundred-thousandths
millions	millionths
ten-millions	ten-millionths
hundred-millions	hundred-millionths

Examples

1. The shaded number in 23.148 is in the _____ place. Ans: hundredths

2. The shaded number in 1.596 is in the _____ place. Ans: thousandths

3. The shaded number in 159.19003 is in the _____ place.Ans: hundred-thousandth

Exercises

Click the ? symbol to see the correct answer.

1. The shaded number in 1.234 is in the ? place.	2. The shaded number in 24.568 is in the ? place.
3. The shaded number in 1.098702 is in the ? place.	4. The shaded number in 127.339073 is in the ? place.
5. The shaded number in 3.40008 is in the ? place.

Author: David L. Heiserman
Publisher: SweetHaven Publishing Services