Chapter 3 Decimals Copyright 2008 Pearson AddisonWesley All

Section 3. 1 Understanding Decimals Copyright Addison-Wesley. All rights reserved. Copyright© © 2008 Pearson

Identify the Place Value of a Digit in a Decimals have a whole number

Identify the Place Value of a Digit in a Decimal The place values to

Example Identify the place value of the indicated digit. a. b. c. d. e.

Solution Strategy Identify the place value of the indicated digit. a. 17. 1473 tenths

Write a Decimal in Word Form Copyright © 2008 Pearson Addison-Wesley. All rights reserved.

Example Write each decimal in word form. a. 0. 516 b. 0. 0385 c.

Solution Strategy Write each decimal in word form. a. 0. 516 five hundred sixteen

Solution Strategy Write each decimal in word form. d. 35. 718 thirty-five and seven

Write a Decimal in Standard Form In writing decimals in standard notation, we must

Example Write each decimal in standard form. a. five thousandths b. three hundred fifty-six

Solution Strategy Write each decimal in word form. a. five thousandths = 0. 005

Convert a Decimal to a Fraction Rule for Converting a Decimal to a Fraction

$Example Convert each decimal to a fraction or mixed number. Simplify, if possible. a.$

$Solution Strategy Convert each decimal to a fraction or mixed number. Simplify, if possible.$

Compare Decimals Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -17

Example Insert the symbol <, >, or = to form a true statement. a.

Solution Strategy Insert the symbol <, >, or = to form a true statement.

Round a Decimal to a Specified Place Value Copyright © 2008 Pearson Addison-Wesley. All

Example Round each decimal to the specified place value. a. 7. 269 to the

Solution Strategy Round each decimal to the specified place value. a. 7. 269 to

Example Apply your knowledge a. You are writing a check for one hundred twenty-seven

Solution Strategy a. You are writing a check for one hundred twenty-seven dollars and

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Identify the Place Value of a Digit in a Decimals have a whole number side and a decimal side separated by a dot known as a decimal point. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -3

Identify the Place Value of a Digit in a Decimal The place values to the left of the decimal point are powers of 10 and the place values to the right of the decimal point are fractions whose denominators are powers of 10. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -4

Solution Strategy Identify the place value of the indicated digit. a. 17. 1473 tenths b. 6. 9426 thousandths c. 0. 00345 hundred-thousandths d. 234. 53 hundredths e. 123. 728432 ten-thousandths Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -6

Solution Strategy Write each decimal in word form. a. 0. 516 five hundred sixteen thousandths b. 0. 0385 three hundred eighty-five tenthousandths c. 9. 43 nine and forty-three hundredths Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -9

Solution Strategy Write each decimal in word form. d. 35. 718 thirty-five and seven hundred eighteen thousandths e. 324. 1839 three hundred twenty-four and one thousand eight hundred thirtynine ten-thousandths Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -10

Write a Decimal in Standard Form In writing decimals in standard notation, we must make sure that the last digit is in the correct place. We do so by inserting zeros as placeholders when necessary. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -11

Example Write each decimal in standard form. a. five thousandths b. three hundred fifty-six and forty-one thousandths c. thirty-eight and four hundred ninety-eight tenthousandths Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -12

Solution Strategy Write each decimal in word form. a. five thousandths = 0. 005 b. three hundred fifty-six and forty-one thousandths = 356. 041 c. thirty-eight and four hundred ninety-eight ten-thousandths = 38. 0498 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -13

Convert a Decimal to a Fraction Rule for Converting a Decimal to a Fraction To convert a decimal to a fraction, write the whole number formed by the digits to the right of the decimal point as the numerator, and write the power of 10 that has as many zeros as place values in the decimal as the denominator. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -14

$Example Convert each decimal to a fraction or mixed number. Simplify, if possible. a.$

$Solution Strategy Convert each decimal to a fraction or mixed number. Simplify, if possible.$

Example Round each decimal to the specified place value. a. 7. 269 to the nearest tenth b. 0. 053866 to the nearest hundredth c. 0. 053866 to the nearest thousandth d. 0. 053866 to the nearest ten-thousandth Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -21

Solution Strategy Round each decimal to the specified place value. a. 7. 269 to the nearest tenth = 7. 3 b. 0. 49716 to the nearest hundredth = 0. 50 c. 0. 12345 to the nearest thousandth = 0. 123 d. 0. 00985 to the nearest ten-thousandth = 0. 0099 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -22

Example Apply your knowledge a. You are writing a check for one hundred twenty-seven dollars and eight cents. Write the decimal notation for this. b. You are writing a check for $283. 56. Write the word form for this amount. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -23

Solution Strategy a. You are writing a check for one hundred twenty-seven dollars and eight cents. Write the decimal notation for this. $127. 08 b. You are writing a check for $283. 56. Write the word form for this. Two hundred eighty-three dollars and fifty-six cents. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 3 -1 -24