Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Chapter 4 Decimals

Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 4.1 Introduction to Decimals

33 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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.

44 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Writing and Reading Decimals in Words

55 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Writing a Decimal in Words Write the decimal in words one hundred forty-threeandfifty-six thousandths whole number part decimal part

66 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write the decimals in words. a.3.6 three and six tenths b one hundred twenty-four and fifty- two hundredths

77 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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 decimal partwhole-number partdecimal 5 must be in the hundredths place 5 must be in the hundredths place

88 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write each decimal in standard form. a.Twelve and six hundredths b.Fifty-four and seventy-two thousandths

99 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Writing Decimals as Fractions DecimalIn WordsFraction 0.5 five tenths 0.36 thirty-six hundredths two thousandths 0.07 seven hundredths

10 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write the decimals as a fraction or mixed number. a.0.9 b decimal place1 zero 3 decimal places3 zeros

11 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Examples Write each fraction as a decimal. a. = 0.6 b. = decimal place 1 zero 3 decimal places 3 zeros

12 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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  2 decimal places 2 zeros  3 decimal places 3 zeros Comparing Two Positive Decimals

13 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Comparing Decimals One way to compare decimals is to compare their graphs on a number line. Recall that for any two numbers on a number line, the number to the left is smaller and the number to the right is larger. To compare 0.3 and 0.7 look at their graphs

14 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Comparing decimals by comparing their graphs on a number line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places. Comparing Two Positive Decimals

15 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Comparing Two Positive Decimals 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. 3 5 < <

16 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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 on When 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

17 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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, rounded to the nearest hundredth is Rounding Decimals

18 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. 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.

19 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Rounding Decimals to a Place Value Round to the nearest tenth. Locate the digit to the right of the tenths place tenths place digit to the right Since the digit to the right is less than 5, drop it and all digits to its right rounded to the nearest tenths is 326.4

20 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Round to the nearest thousandth. Step 1: Locate the digit to the right of the given place value 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 rounded to the nearest thousandth is 0.594

21 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example Round $0.067 to the nearest cent. Step 1: Locate the digit to the right of the given place value. $ 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.

22 Copyright © 2012 Pearson Education, Inc. Publishing as Prentice Hall. Example An aquarium cats $ Round the price to the nearest dollar. The nearest dollar means the ones place. Locate the digit to the right of the ones place. $ is to the right of the ones place value Thus $ rounds to $