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Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 4 Objectives 1.Write decimals as fractions. 2.Add and subtract decimals. 3.Multiply and divide decimals. 4.Write fractions as decimals. 5.Convert percents to decimals and decimals to percents. 6.Use fraction, decimal, and percent equivalents. R.2 Decimals and Percents

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 5 R.2 Decimals and Fractions Converting a Decimal to a Fraction Read the name using the correct place value. Write it in fraction form just as you read it. The denominator will be a power of 10, a number like 10, 100, 1000, and so on. Writing Decimals as Fractions

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 6 Example 1 Write each decimal as a fraction. Do not write in lowest terms. (a) 0.85 This is read “85 hundredths.” So (b) 0.029 This is read “29 thousandths.” So (c) 3.5907 This is read “3 and 5907 ten-thousandths”. So R.2 Decimals and Fractions Writing Decimals as Fractions

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 7 + Example 2 Add or subtract as indicated. (a) 13.129 + 0.25 + 5.6 R.2 Decimals and Fractions Adding and Subtracting Decimals Add decimals in a column. Make sure the decimal points line up. Attach zeros to make all the numbers the same length. – (b) 2 – 0.329 Rewrite the operation in a column. Attach zeros.

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 8 R.2 Decimals and Fractions Multiplying and Dividing Decimals Multiplying Decimals Ignore the decimal points and multiply as if the numbers were whole numbers. Then add together the number of decimal places (digits to the right of the decimal point) in each number being multiplied. Place the decimal point in the answer that many digits from the right.

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 9 Example 3 Multiply. 12.3 × 9.18 R.2 Decimals and Fractions Multiplying and Dividing Decimals × 1 decimal place 2 decimal places 1 + 2 = 3 3 decimal places

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 10 R.2 Decimals and Fractions Multiplying and Dividing Decimals Dividing Decimals Change the divisor (the number you are dividing by) into a whole number by moving the decimal point as many places as necessary to the right. Move the decimal point in the dividend (the number you are dividing into) to the right by the same number of places. Move the decimal point straight up and then divide as with whole numbers. Dividend Quotient Divisor

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 11 0 Example 4 Divide. R.2 Decimals and Fractions Multiplying and Dividing Decimals 12.5 0.25 So, 12.5 0.25 = 50

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 12 Multiplying or Dividing by Powers of 10 To multiply by a power of 10, move the decimal point to the right as many places as the number of zeros. To divide by a power of 10, move the decimal point to the left as many places as the number of zeros. In both cases, insert 0s as placeholders if necessary. R.2 Decimals and Fractions Multiplying and Dividing Decimals

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 13 Example 5 Multiply or divide as indicated. R.2 Decimals and Fractions Multiplying and Dividing Decimals We moved the decimal point three places to the right because 1000 has three zeros. We moved the decimal point four places to the left because 10,000 has four zeros. We needed to insert a zero in front of the 8 to do this.

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 14 Rule for Rounding If the digit to become 0 or be dropped is 5 or more, round up by adding 1 to the final digit to be kept. If the digit to become 0 or be dropped is 4 or less, do not round up. R.2 Decimals and Fractions Multiplying and Dividing Decimals

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 15 Writing a Fraction as a Decimal Because a fraction bar indicates division, write a fraction as a decimal by dividing the denominator into the numerator. R.2 Decimals and Fractions Writing Fractions as Decimals

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 16 Example 6 Write as a decimal. R.2 Decimals and Fractions Writing Fractions as Decimals = 1.5625

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 17 R.2 Decimals and Fractions Converting Percents to Decimals and Decimals to Percents 1% = 0.01 or 1% = Example 7 Write 65% as a decimal. 65% = 65 · 1% = 65 · 0.01= 0.65

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 18 Note A quick way to change from a percent to a decimal is to move the decimal point two places to the left and drop the % symbol. To change from a decimal to a percent, move the decimal point two places to the right and attach a percent symbol. DecimalPercent R.2 Decimals and Fractions Converting Percents to Decimals and Decimals to Percents Multiply by 100; Move 2 places right. Divide by 100; Move 2 places left.

Copyright © 2010 Pearson Education, Inc. All rights reserved. R.2 – Slide 19 = 32. Example 8 Convert each percent to a decimal and each decimal to a percent. R.1 Fractions Multiplying and Dividing Fractions a) 32%= 0.32 b) 175%= 175.= 1.75 c) 0.95= 0.95= 95% d) 3.15= 3.15= 315%