3 1 Decimal Notation Order and Rounding OBJECTIVES

3. 1 Decimal Notation, Order, and Rounding OBJECTIVES a Given decimal notation, write a word name. b Convert between decimal notation and fraction notation. c Given a pair of numbers in decimal notation, tell which is larger. d Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 1

3. 1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 2

3. 1 Decimal Notation, Order, and Rounding Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 3

3. 1 Decimal Notation, Order, and Rounding a Given decimal notation, write a word name. EXAMPLE 4 Write a word name for 1788. 045. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 4

3. 1 Decimal Notation, Order, and Rounding Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 5

3. 1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. EXAMPLE 5 Write fraction notation for 0. 876. Do not simplify. For a number like 0. 876, we generally write a 0 before the decimal point to draw attention to the presence of the decimal point. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 6

3. 1 Decimal Notation, Order, and Rounding To convert from fraction notation to decimal notation when the denominator is 10, 1000, and so on, a) count the number of zeros, and b) move the decimal point that number of places to the left. Leave off the denominator. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 7

3. 1 Decimal Notation, Order, and Rounding Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 8

3. 1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. EXAMPLE 8 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 9

3. 1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. If a mixed numeral has a fractional part with a denominator that is a power of ten, such as 10, 100, or 1000, and so on, we first write the mixed numeral as a sum of a whole number and a fraction. Then we convert to decimal notation. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 10

3. 1 Decimal Notation, Order, and Rounding b Convert between decimal notation and fraction notation. EXAMPLE 12 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 11

3. 1 Decimal Notation, Order, and Rounding To compare two numbers in decimal notation, start at the left and compare corresponding digits moving from left to right. If two digits differ, the number with the larger digit is the larger of the two numbers. To ease the comparison, extra zeros can be written to the right of the last decimal place. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 12

3. 1 c Decimal Notation, Order, and Rounding Given a pair of numbers in decimal notation, tell which is larger. EXAMPLE 15 Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 13

3. 1 Decimal Notation, Order, and Rounding To round to a certain place: a) Locate the digit in that place. b) Consider the next digit to the right. c) If the digit to the right is 5 or higher, round up. If the digit to the right is 4 or lower, round down. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 14

3. 1 d Decimal Notation, Order, and Rounding Round decimal notation to the nearest thousandth, hundredth, tenth, one, ten, hundred, or thousand. EXAMPLE 18 Round 3872. 2459 to the nearest thousandth, hundredth, tenth, one, ten, hundred, and thousand. Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc. Slide 15