Chapter R Prealgebra Review Decimal Notation R DECIMAL

Chapter R Prealgebra Review Decimal Notation

$R. DECIMAL NOTATION 3 a. Convert from decimal notation to fraction notation. b. Add,$

R. DECIMAL NOTATION 3 a. Convert from decimal notation to fraction notation. b. Add, subtract, multiply, and divide using decimal notation. c. Round numbers to a specified decimal place.

4 2 . 3 2 4 5 The decimal notation 42. 3245 means 4 tens + 2 ones + 3 tenths + 2 hundredths + 4 thousandths + 5 ten-thousandths We read this number as: “Forty-two and three thousand two hundred forty-five ten-thousandths. ” The decimal point is read as “and”.

$To convert from decimal to fraction notation: a) Count the number of decimal places.$

To convert from decimal to fraction notation: a) Count the number of decimal places. 4. 98 2 places b) Move the decimal point that many places to the right. 4. 98 Move 2 places. c) Write the result over a denominator with that number of zeros. 2 zeros

$Example Write fraction notation for 0. 924. Do not simplify. Solution 0. 924 Copyright$

$Example Write fraction notation for 0. 924. Do not simplify. Solution 0. 924. 3$

$Example Write 17. 77 as a fraction and as a mixed numeral. Solution To$

Example Write 17. 77 as a fraction and as a mixed numeral. Solution To write as a fraction: 17. 77. 2 places 2 zeros To write as a mixed numeral, we rewrite the whole number part and express the rest in fraction form: Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 7

$To convert from fraction notation to decimal notation when the denominator is 10, 1000$

To convert from fraction notation to decimal notation when the denominator is 10, 1000 and so on, a) Count the number of zeros. 3 zeros b) Move the decimal point that number of places to the left. Leave 8. 679. off the denominator. Move 3 places.

Example Write decimal notation for Solution 1 zero 1 place Copyright © 2015, 2011,

Adding with decimal notation is similar to adding whole numbers. First we line up the decimal points in addition so that we can add corresponding place-value digits. Add the digits from the right. If necessary, we can write extra zeros to the far right of the decimal point so that the number of places is the same. Place the decimal point in the answer in line with decimal points in numbers.

Example Add: 4. 31 + 0. 146 + 14. 2 Subtract: 34. 07 –

Example Add: 4. 31 + 0. 146 + 14. 2 Solution: Line up the

Example Subtract: 34. 07 – 4. 0052 Solution Line up decimal points and subtract, borrowing if necessary. 6 9 10 3 4. 0 7 0 0 – 4. 0 0 5 2 3 0. 0 64 8 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 13

Example Subtract 574 – 3. 825 Solution 3 9 9 10 5 7 4.

Multiplication with Decimal Notation a) Ignore the decimal points, and multiply as whole numbers. b) Place the decimal point in the result of step (a) by adding the number of decimal places in the original factors.

Example Multiply 7. 3 85. 1. Copyright © 2015, 2011, and 2007 Pearson Education,

Example Multiply 7. 3 85. 1. Solution Ignore the decimal points and multiply as if both factors are integers then place the decimal point. 3 1 85. 1 7. 3 2553 59570 6 2 1. 2 3 1 decimal place 2 decimal places Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 17

Dividing When the Divisor is a Whole Number a) Place the decimal point in the quotient directly above the decimal point in the dividend. b) Divide as whole numbers.

Example Divide 91. 26 26. Copyright © 2015, 2011, and 2007 Pearson Education, Inc.

Example Divide 91. 26 26. place the decimal point Solution Copyright © 2015, 2011,

Dividing When the Divisor is Not a Whole Number a) Move the decimal point in the divisor as many places to the right as it takes to make it a whole number. Move the decimal point in the dividend the same number of places to the right and place the decimal point in the quotient. b) Divide as whole numbers, inserting zeros if necessary.

Example Divide: 7. 872 9. 6. Copyright © 2015, 2011, and 2007 Pearson Education,

Example Divide: 7. 872 9. 6. Solution Move the decimal point in the divisor 1 place to the right. Move the decimal point in the dividend 1 place to the right. 7. 872 9. 6 = 0. 82. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 23

Example Find decimal notation for Copyright © 2015, 2011, and 2007 Pearson Education, Inc.

Example Find decimal notation for Solution You might also divide 7 by 25 to

Example Find decimal notation for Solution Divide 1 12 Since 4 keeps reappearing as a remainder, the digit 3 will continue to repeat in the quotient; therefore, The dots indicate an endless sequence of digits in the quotient. The dots are often replaced by a bar to indicate the repeating part. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 26

Example Find decimal notation for Solution 5 11 Since 6 and 5 keep reappearing as remainders, the sequence of digits “ 45” repeats in the quotient, and Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 27

Rounding Decimal Notation To round to a certain place: a) Locate the digit in that place. b) Consider the digit to its right. c) If the digit to the right is 5 or higher, round up, if the digit to the right is less than 5, round down.

Example Round 0. 072 to the nearest tenth. Round 34. 7824 to the nearest hundredth. Round 478. 3469 to the nearest thousandth, hundredth, tenth, ones, tens, hundreds, and thousands. Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 29

Example Round 0. 072 to the nearest tenth. Solution a. Locate the digit in the tenths place. 0. 072 b. Consider the next digit to the right. c. Since that digit, 7 is greater than 5, round up: 0. 1 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 30

Example Round 34. 7824 to the nearest hundredth. Solution a. Locate the digit in the hundredths place. 34. 7824 b. Consider the next digit to the right. c. Since that digit, 2 is less than 5, we round down: 34. 78 Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 31

Example Round 478. 3469 to the nearest thousandth, hundredth, tenth, ones, tens, hundreds, and thousands. Solution 4 7 8. 3 4 6 9 thousandth hundredth tenth 4 4 4 7 7 7 8 8 8 . . . one ten hundred thousand 4 4 5 7 8 0 0 0 . . Copyright © 2015, 2011, and 2007 Pearson Education, Inc. 3 3 3 4 5 7 32