Basic Mathematics for College Students

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CHAPTER 4 SUMMARY AND REVIEW

SECTION 4.1 An Introduction to Decimals

The place-value system for whole numbers can

be extended to create the decimal numeration

system.

The place-value columns to the left of the decimal

point form the whole-number partof the decimal

number. The value of each of those columns is 10

times greater than the column directly to its right.

The columns to the right of the decimal point form

the fractional part.Each of those columns has a

value that is of the value of the place directly to

its left.

1

10

To write a decimal number in expanded form

(expanded notation) means to write it as an

addition of the place values of each of its digits.

Write 28. 9341 in expanded notation:

28.9341 20  8 

9

10



3

100



4

1,000



1

10,000

DEFINITIONS AND CONCEPTS EXAMPLES

The place value of the digit 3 is 3 hundredths.

The digit that tells the number of ten-thousandthsis 1.

To read a decimal:

1.Look to the left of the decimal point and say

the name of the whole number.

2.The decimal point is read as “and.”

3.Say the fractional part of the decimal as a

whole number followed by the name of the last

place-value column of the digit that is the

farthest to the right.

We can use the steps for reading a decimal to write

it in words.

Write the decimal in words and then as a fraction or mixed number:

28. 9341 The whole-number part is 28. The fractional part is 9341.

The digit the farthest to the right, 1, is in the ten-

thousandths place.

Twenty-eight and nine thousand three hundred forty-one

ten-thousandths

Written as a mixed number, 28.9341 is.

Write the decimal in words and then as a fraction or mixed number:

0. 079 The whole-number part is 0. The fractional part is 79. The

digit the farthest to the right, 9, is in the thousandths place.

Seventy-nine thousandths

Written as a fraction, 0.079 is.

79

1,000

28

9,341

10,000

The procedure for reading a decimalcan be applied

in reverse to convert from written-word form to

standard form.

Write the decimal number in standard form:

Negative twelve and sixty-five ten-thousandths

This is the ten-thousandths place-value column.

Two place holder 0’s must be inserted here so

that the last digit in 65 is in the ten-

thousandths column.

12.0065

2.9 8

Decimal point

Ten

ths

HundredsTens

3 41

Hu

ndred-thousand

ths

Ten-thousand

ths

Hundred

ths

Ones

Thousands Thousand

ths

Whole-number part

1,000 100 10 1 –– 101 100 –––^1 1,000––––^1 10,000–––––^1 100,000––––––^1

Fractional part