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Decimals

Chapter 5. Decimals. Introduction to Decimals. 5.1. Decimal Notation. 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. 16.743.

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Decimals

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  1. Chapter 5 Decimals

  2. Introduction to Decimals 5.1

  3. Decimal Notation 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. 16.743 Whole number part Decimal part Decimal point

  4. Place Value 1 1 1 10 1000 100,000 1 1 100 10,000 The position of each digit in a number determines its place value. hundred-thousandths hundreds tens tenths hundredths thousandths ten-thousandths ones 1 6 7 3 4 100 10 1 Place Value decimal point

  5. Place Value 1 10 Notice that the value of each place is of the value of the place to its left.

  6. 16.734 Place Value 3 100 The digit 3 is in the hundredths place, so its value is 3 hundredths or .

  7. Writing 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.

  8. Writing a Decimal in Words decimal part whole number part Write the decimal 143.056 in words. 143.056 one hundred forty-three and fifty-six thousandths

  9. A decimal written in words can be written in standard form by reversing the procedure. Writing Decimals in Standard Form whole-number part decimal decimal part Write one hundred six and five hundredths in standard form. one hundred six and five hundredths 5 must be in the hundredths place 106 . 05

  10. Helpful Hint thousandths place 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. For example, three and fifty-four thousandths is 3.054

  11. Writing Decimals as Fractions 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 is read “nine tenths” and written as a fraction as

  12. Writing Decimals as Fractions 21 100 11 1000 0.21 is read as twenty-one hundredths and written as a fraction as 0.011 is read as eleven thousandths and written as a fraction as

  13. Comparing Two Positive Decimals 37 29 = 0 . 37 = 0 . 029 100 1000 2 zeros 3 decimal places 3 zeros 2 decimal places 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.

  14. Comparing Decimals 3 7 10 10 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. 0 0.3 0.7 1 0.3 < 0.7 or 0.7 > 0.3

  15. Comparing Two Positive Decimals 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.

  16. 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. 35.638 35.657 5 < 3 35.638 < 35.657

  17. 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

  18. Rounding Decimals 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, 63.782 rounded to the nearest hundredth is 63.78

  19. Rounding Decimals 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.

  20. Rounding Decimals to a Place Value tenths place digit to the right Round 326.4386 to the nearest tenth. Locate the digit to the right of the tenths place. 326.4386 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

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