Chapter 2 Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved. Decimals

Lesson 2.1 Reading, Determining the Value of, Adding, Subtracting, and Multiplying a Decimal 1. Reading and writing decimal numbers 2. Determining the value of decimal fractions 3. Adding, subtracting, multiplying, and dividing decimals 4. Multiplying and dividing decimals by 10 or a power of 10 5. Multiplying and dividing decimals by 0.1 or a multiple of 0.1 Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Decimal Numbers For example: 23.405 Writing decimal numbers Reading decimal numbers For example: 23.405 Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Decimal Fractions Place decimal numbers in a vertical column with aligned decimal points. For example: 7.45 0.206 34.2 Of 0.75, 0.235, and 0.008, which decimal fraction has the greatest value? Of 1.5, 1.007, 0.95, and 0.432, which decimal fraction has the least value? Of 0.75, 0.235, and 0.008, which decimal fraction has the greatest value? Compare the numbers to the right of the decimal point for all fractions. In this case, 0.75 has the greatest value because 7 is larger than 2 and 0. Of 1.5, 1.007, 0.95, and 0.432, which decimal fraction has the least value? Start by comparing the whole numbers to the left of the decimal point. Then compare the numbers to the right of the decimal point. In this case, 0.432 has the least (smallest) value.   Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Adding and Subtracting Decimals (1 of 2) Place decimal numbers in a vertical column with aligned decimal points. Add zeros to complete the columns as needed. Add or subtract each column as indicated. Place the decimal point in the sum or difference. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Adding and Subtracting Decimals (2 of 2) For examples: Add: 13.75 + 2.1 + 4.08 Subtract: 0.807 − 0.51 Add: 13.75 + 2.1 + 4.08 Add these numbers. Remember to place the decimal point for the sum directly below the decimal points in the column. The sum is 19.93. Subtract: 0.807 − 0.51 Subtract 0.51 from 0.807. Remember to place the decimal point for the sum directly below the decimal points in the column. The difference is 0.297. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Multiplying Decimals (1 of 2) Place the decimal number with the fewer digits underneath the other number. Multiply the decimal numbers as if the decimals were not present. Count the number of digits to the right of the decimal point for each decimal number being multiplied. Place the decimal point in the final number. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Multiplying Decimals (2 of 2) For examples: Multiply: 13.75 × 2.1 Multiply: 0.807 × 0.51 Multiply: 13.75 × 2.1 The number of digits to the right of the decimal point is 3, and the answer is 28.875. Note: It is possible to check your answer by estimating what you expect to get using whole numbers. If you round 13.75 up to 14 and 2.1 down to 2, then you can multiply 14 and 2 to get 28. Therefore, the final answer seems reasonable. Multiply: 0.807 × 0.51 The number of digits to the right of the decimal point is 5, and the answer is 0.41157. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Multiplying a Decimal by 10 or a Power of 10 Move the decimal point to the right when multiplying. For example: 0.458 × 10,000 When multiplying a decimal number by a power of 10, move the decimal point to the right by the same number of spaces as the number of zeros in the multiplier (power of 10). Multiply: 0.458 × 10,000 The answer is 4580. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Multiplying a Number by 0.1 or a Multiple of 0.1 Move the decimal point to the left when multiplying. For example: 43.58 × 0.01 When multiplying a decimal number by a multiple of 0.1, move the decimal point to the left by the same number of spaces as there are numbers to the right of the decimal point in the multiplier (multiple of 0.1). Multiply: 43.58 × 0.01 The answer is 0.4358. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Lesson 2.2 Rounding, Dividing, and Converting a Decimal 1. Adding, subtracting, multiplying, and dividing decimals 2. Rounding decimal fractions to an indicated place value 3. Multiplying and dividing decimals by 10 or a power of 10 4. Multiplying and dividing decimals by 0.1 or a multiple of 0.1 5. Converting a decimal fraction to a proper fraction 6. Converting a proper fraction to a decimal fraction Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Rounding a Decimal Fraction (1 of 2) Find the number to the right of the place value desired. If the number is 5, 6, 7, 8, or 9, add 1 to the number in the place value desired. If the number is 0, 1, 2, 3, or 4, drop numbers to the right. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Rounding a Decimal Fraction (2 of 2) For examples: Round 1.355 to the nearest tenth. Round 0.8009 to the nearest hundredth. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Dividing Decimals (1 of 3) Place a caret (^) to the right of the last number in the divisor. Count the number of digits between the decimal point and the decimal in the divisor. Place a caret (^) in the dividend. The technique here is to divide whole numbers rather than decimal numbers. So, first you need to determine which decimal number has more digits to the right of the decimal point. Then place a caret to the right of each decimal number, but the caret should be the same number of spaces to the right of the decimal place for each decimal number. It might be necessary to add zeros to the right of the decimal numbers when placing the caret the correct number of spaces to the right of the decimal point. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Dividing Decimals (2 of 3) Place a decimal point on the quotient line directly above the caret (^). Divide, extending the decimal fraction three places to the right of the decimal point. Zeros may be added to extend the decimal fraction dividend. Round the quotient to the nearest hundredth. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Dividing Decimals (3 of 3) For examples: Divide: 13.75 ÷ 2.1 Divide: 0.87 ÷ 0.517 Divide: 13.75 ÷ 2.1 In this example, 13.75 would become 13.75^, and 2.1 would become 2.10^ (note that a 0 had to be added to 2.1). The answer, rounded to the nearest hundredth, is 6.55 (rounding up from 6.547). Divide: 0.87 ÷ 0.517 In this example, 0.517 would become 0.517^, and 0.87 would become 0.870^ (note that a 0 had to be added to 0.87). The answer, rounded to the nearest hundredth, is 1.68 (rounding down from 1.682). Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Dividing a Decimal by 10 or a Multiple of 10 Move the decimal point to the left when dividing. For example: Divide: 2.56 ÷ 100 Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Dividing a Number by 0.1 or a Multiple of 0.1 Move the decimal point to the right when dividing. For example: Divide: 2.56 ÷ 0.001 When dividing a decimal number by a multiple of 0.1, move the decimal point to the right by the same number of spaces because there are numbers to the right of the decimal point in the divisor (multiple of 0.1). Divide: 2.56 ÷ 0.001 The answer is 2560. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Converting a Decimal Fraction to a Proper Fraction (1 of 2) Remove the decimal point and the zero to the left of it. Determine the numerator. Determine the denominator. Reduce to lowest terms. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Converting a Decimal Fraction to a Proper Fraction (2 of 2) For example: Convert: 0.35 Convert: 0.35 In this case, the numerator is 35, and the denominator is 100. That makes the final answer 35/100. (This proper fraction can be reduced to 7/20.) Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Converting a Proper Fraction to a Decimal Fraction (1 of 2) Divide the numerator by the denominator. Extend the decimal fraction to the desired number of places. Be sure to place a zero to the left of the decimal point. Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.

Converting a Proper Fraction to a Decimal Fraction (2 of 2) For examples: Convert: 1 3 Convert: 9 11 Copyright © 2020 by Mosby, an imprint of Elsevier Inc. All rights reserved.