2. Decimals Chapter Five

3. Introduction to Decimals Section 5.1

4. Whole- number part Decimal point Decimal part 16.743 Like fractional notation, decimal notation is used to denote a part of a whole. Numbers written in decimal notation are called decimal numbers, or simply decimals. The decimal 16.734 has three parts. 3

5. The position of each digit in a number determines its place value. 1 6 7 3 4 onesthousandthshundredstenstenthshundredthsten-thousandthshundred-thousandths Place Value decimal point 10010 1 1 100 1 10,000 1 10 1 100,000 1 1000 4

6. Notice that the value of each place is of the value of the place to its left. 1 10 5 Martin-Gay, Prealgebra, 5ed

7. 16.734 The digit 3 is in the hundredths place, so its value is 3 hundredths or. its value is 3 hundredths or. 3 100 6 Martin-Gay, Prealgebra, 5ed

8. Writing (or Reading) a Decimal in Words Step 1. Write the whole-number part in words. Step 2. Write “and” for the decimal point. Step 3. Write the decimal part in words as though it were a whole number, followed by the place value of the last digit. 7 Martin-Gay, Prealgebra, 5ed

9. Writing a Decimal in Words Write the decimal 143.056 in words. 143.056 one hundred forty-threeandfifty-six thousandths whole-number part decimal part 8 Martin-Gay, Prealgebra, 5ed

10. A decimal written in words can be written in standard form by reversing the procedure. Writing Decimals in Standard Form Write one hundred six and five hundredths in standard form. one hundred six and five hundredths 106.05 decimal partwhole-number partdecimal 5 must be in the hundredths place 5 must be in the hundredths place 9

11. Helpful Hint b When writing a decimal from words to decimal notation, make sure the last digit is in the correct place by inserting 0s after the decimal point if necessary. b For example, three and fifty-four thousandths is 3.054 thousandths place 10 Martin-Gay, Prealgebra, 5ed

12. Once you master writing and reading decimals correctly, then you write a decimal as a fraction using the fractions associated with the words you use when you read it. 0.9 0.9 is read “nine tenths” and written as a fraction as Writing Decimals as Fractions 11 Martin-Gay, Prealgebra, 5ed

13. twenty-one hundredths and written as a fraction as 21100 0.011 is read as eleven thousandths and written as a fraction as 111000 0.21 is read as 12 Martin-Gay, Prealgebra, 5ed

14. Notice that the number of decimal places in a decimal number is the same as the number of zeros in the denominator of the equivalent fraction. We can use this fact to write decimals as fractions. 037 100.  2 decimal places 2 zeros 0029 29 1000.  3 decimal places 3 zeros 13

15. Comparing Decimals One way to compare decimals is to compare their graphs on a number line. Recall that for any two numbers on a number line, the number to the left is smaller and the number to the right is larger. To compare 0.3 and 0.7 look at their graphs. 01 0.3 3 10 7 0.7 0.3 14 Martin-Gay, Prealgebra, 5ed

16. Comparing decimals by comparing their graphs on a number line can be time consuming, so we compare the size of decimals by comparing digits in corresponding places. 15 Martin-Gay, Prealgebra, 5ed

17. Comparing Two Positive Decimals Compare digits in the same places from left to right. When two digits are not equal, the number with the larger digit is the larger decimal. If necessary, insert 0s after the last digit to the right of the decimal point to continue comparing. Compare hundredths place digits 35 < 35.63835.657< 35.63835.657 16 Martin-Gay, Prealgebra, 5ed

18. Helpful Hint For any decimal, writing 0s after the last digit to the right of the decimal point does not change the value of the number. 8.5 = 8.50 = 8.500, and so on When a whole number is written as a decimal, the decimal point is placed to the right of the ones digit. 15 = 15.0 = 15.00, and so on 15 = 15.0 = 15.00, and so on 17 Martin-Gay, Prealgebra, 5ed

19. We round the decimal part of a decimal number in nearly the same way as we round whole numbers. The only difference is that we drop digits to the right of the rounding place, instead of replacing these digits by 0s. For example, Rounding Decimals 63.782 rounded to the nearest hundredth is 63.78 18 Martin-Gay, Prealgebra, 5ed

20. Rounding Decimals To a Place Value to the Right of the Decimal Point Step 1. Locate the digit to the right of the given place value. Step 2. If this digit is 5 or greater, add 1 to the digit in the given place value and drop all digits to the right. If this digit is less than 5, drop all digits to the right of the given place. 19 Martin-Gay, Prealgebra, 5ed

21. Rounding Decimals to a Place Value Round 326.4386 to the nearest tenth. Locate the digit to the right of the tenths place. 326.4386 tenths place digit to the right Since the digit to the right is less than 5, drop it and all digits to its right. 326.4386 rounded to the nearest tenths is 326.4 20 Martin-Gay, Prealgebra, 5ed