OBJECTIVES

3.1 Decimal Notation, Order, and Rounding

dUse < or > for to write a true statement in a situation like 6 10.

Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

3.1 Decimal Notation, Order, and Rounding

a Given decimal notation, write a word name.

Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3.1 Decimal Notation, Order, and Rounding

aGiven decimal notation,

write a word name.

Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

a Given decimal notation, write a word name.

4

Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Write a word name for 1788.045.

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

5

Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

To convert from fraction notation to decimal notation when the denominator is 10, 100, 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.

3.1 Decimal Notation, Order, and Rounding

bConvert between decimal notation and fraction notation.

Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

8

Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

b Convert between decimal notation and fraction notation.

12

Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3.1 Decimal Notation, Order, and Rounding

cGiven a pair of numbers in decimal notation, tell which is larger.

Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

c Given a pair of numbers in decimal notation, tell which is larger.

15

Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

3.1 Decimal Notation, Order, and Rounding

dRound decimal notation

to the nearest thousandth,

hundredth, tenth, one, ten, hundred, or thousand.

Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

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.

EXAMPLE

3.1 Decimal Notation, Order, and Rounding

d Round decimal notation to the nearest thousandth,hundredth, tenth, one, ten, hundred, or thousand.

18

Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.

Round 3872.2459 to the nearest thousandth, hundredth,tenth, one, ten, hundred, and thousand.