Introduction to Decimals Section 3.1 Introduction to Decimals

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. Objective A

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. Objective A 3

Example Write the decimal 143.056 in words. 143.056 whole number part decimal part one hundred forty-three and fifty-six thousandths

Examples Write each decimal in words. 0.06 six hundredths –124. 52 0.0829 six hundredths negative one hundred twenty-four and fifty- two hundredths Objective A eight hundred twenty-nine ten thousandths 5

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

Writing Decimals in Standard Form A decimal written in words can be written in standard form by reversing the procedure. Write one hundred six and five hundredths in standard form. one hundred six and five hundredths whole-number part decimal decimal part 5 must be in the hundredths place 106 . 05

Examples Write each decimal in standard form. Twelve and six hundredths 12.06 Fifty-four and seventy-two thousandths 54.072 Objective A

Writing Decimals as Fractions In Words Fraction 0.5 five tenths 0.36 thirty-six hundredths 0.002 two thousandths 0.07 seven hundredths Objective A 9

Examples Write the decimals as a fraction or mixed number. 0.9 21.094 1 decimal place 1 zero Objective A 3 decimal places 3 zeros 10

Examples Write each decimal as a fraction or a mixed number. Write your answer in simplest form. 0.12 64.8 –209.986 Objective A 11

Comparing Two Positive Decimals 37 100 . = 029 29 1000 . = 2 decimal places 2 zeros 3 decimal places 3 zeros 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.

Comparing Two Positive Decimals Chapter 1 / Whole Numbers and Introduction to Algebra 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 28.253 28.263 5 < 6 so 28.253 < 28.263

Chapter 1 / Whole Numbers and Introduction to Algebra Helpful Hint 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

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

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

Chapter 1 / Whole Numbers and Introduction to Algebra Rounding Decimals 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

Chapter 1 / Whole Numbers and Introduction to Algebra Rounding Decimals Chapter 1 / Whole Numbers and Introduction to Algebra 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.

Example Round 326.4386 to the nearest tenth. Locate the digit to the right of the tenths place. tenths place 326.4386 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

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 Objective A 20

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. Objective A 21

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. Objective A 22

Example Water 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.