Slide 1Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Introduction to Decimals

Section 3.1

Slide 2Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Decimal Notation and Writing Decimals in Words

Like fractional notation, decimal notation is used to denote a part of a whole. Numbers written in decimal notation are called decimal numbers, or simply decimals. Place names and place values for the decimal parts are also shown.

Slide 3Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Writing and Reading Decimals in Words

Step 1: Write the whole number part in words.

Step 2: Write “and” for the decimal point.

Step 3: Write the decimal part in words as though it were a whole number, followed by the place value of the last digit.

Slide 4Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Write the decimal 143.056 in words.

143.056

one hundred forty-three and fifty-six thousandths

whole number part decimal part

Slide 5Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Examples

Write each decimal in words.

a. 0.06

b. –124. 52

c. 0.0829

six hundredths

negative one hundred twenty-four and fifty- two hundredths

eight hundred twenty-nine ten thousandths

Slide 6Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Examples

Write the decimals in words.

a. 87.31

b. 52.1085

eighty-seven and thirty-one hundredths

fifty-two and one thousand eighty-five ten-thousandths

Slide 7Copyright © 2015, 2011, 2008 Pearson Education, Inc.

A decimal written in words can be written in standard form by reversing the procedure.

Writing Decimals in Standard Form

Write one hundred six and five hundredths in standard form.

one hundred six and five hundredths

106 . 05

decimal partwhole-number part decimal

5 must be in thehundredths place

5 must be in thehundredths place

Slide 8Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Examples

Write each decimal in standard form.

a. Twelve and six hundredths

12.06

b. Fifty-four and seventy-two thousandths

54.072

Slide 9Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Writing Decimals as Fractions

Decimal In Words Fraction

0.5 five tenths

0.36 thirty-six hundredths

0.002 two thousandths

0.07 seven hundredths

5

10

36

1002

1000

7

100

Slide 10Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Examples

Write the decimals as a fraction or mixed number.

a. 0.9

b. 21.094

9

10

1 decimal place 1 zero

9421

1000

3 decimal places 3 zeros

Slide 11Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Examples

Write each decimal as a fraction or a mixed number. Write your answer in simplest form.

a.0.12

b.64.8

c.–209.986

12

100

4 3

4 25

3

25

864

10 2 4

642 5

4

645

986209

1000

2 493209

2 500

493

209500

Slide 12Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Notice that the number of decimal places in a decimal number is the same as the number of zeros in the denominator of the equivalent fraction. We can use this fact to write decimals as fractions.

0 3737

100.

2 decimal places

2 zeros

0 02929

1000.

3 decimal places

3 zeros

Comparing Two Positive Decimals

Slide 13Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Compare digits in the same places from left to right. When two digits are not equal, the number with the larger digit is the larger decimal. If necessary, insert 0s after the last digit to the right of the decimal point to continue comparing.

Compare hundredths place digits

28.253 28.263

5 < 6

so 28.253 < 28.263

Comparing Two Positive Decimals

Slide 14Copyright © 2015, 2011, 2008 Pearson Education, Inc.

For any decimal, writing 0s after the last digit to the right of the decimal point does not change the value of the number.

8.5 = 8.50 = 8.500, and so onWhen a whole number is written as a decimal, the decimal point is placed to the right of the ones digit. 15 = 15.0 = 15.00, and so on

Helpful Hint

Slide 15Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Insert <, >, or = to form a true statement.

26.208 26.28

Add a zero. 26.208 26.280

0 < 8

26.208 < 26.28

Slide 16Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Insert <, >, or = to form a true statement.

0.12 0.026

Add a zero. 0.120 0.026

1 > 0

0.12 > 0.026

Slide 17Copyright © 2015, 2011, 2008 Pearson Education, Inc.

We round the decimal part of a decimal number in nearly the same way as we round whole numbers. The only difference is that we drop digits to the right of the rounding place, instead of replacing these digits by 0s. For example,

63.782 rounded to the nearest hundredth is

63.78

Rounding Decimals

Slide 18Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Rounding Decimals

Step 1: Locate the digit to the right of the given place value.

Step 2: If this digit is 5 or greater, add 1 to the digit in the given place value and drop all digits to the right. If this digit is less than 5, drop all digits to the right of the given place.

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Example

Round 326.4386 to the nearest tenth.

Locate the digit to the right of the tenths place.

326.4386

tenths place

digit to the right

Since the digit to the right is less than 5, drop it and all digits to its right.

326.4386 rounded to the nearest tenth is 326.4

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Example

Round 0.5942 to the nearest thousandth.

Step 1: Locate the digit to the right of the given place value.

0.5942 2 is to the right of the thousandth place value.

Step 2: Since the digit to the right is less than 5, we delete it and all digits to its right.

Thus 0.5942 rounded to the nearest thousandth is 0.594

Slide 21Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

Round $0.067 to the nearest cent.

Step 1: Locate the digit to the right of the given place value.

$0.067 7 is to the right of the hundredths place value

Step 2: Since the digit to the right is more than 5, we round up.

Thus $0.067 rounds to $0.07.

Slide 22Copyright © 2015, 2011, 2008 Pearson Education, Inc.

Example

An aquarium costs $245.69. Round the price to the nearest dollar.

The nearest dollar means the ones place. Locate the digit to the right of the ones place.

$245.69 6 is to the right of the ones place value

Thus $245.69 rounds to $246.00.

Slide 23Copyright © 2015, 2011, 2008 Pearson Education, Inc.

ExampleWater bills in Mexia are always rounded to the nearest dollar. Round a water bill of $24.62 to the nearest dollar.

Rounding to the nearest whole dollar means rounding to the ones place.

24.62 6 is greater than 5

A water bill of $24.62 is rounded to $25.00.