3.1 Place Value and Rounding 1 Decimal Places Digits located to the right of the decimal point occupy decimal places. The decimal places are represented by powers of 10 that would appear in the denominator of equivalent fractions written in fraction form. The first place to the right of the decimal point is the tenths place because it is representative of the common fraction 1/10. Likewise, the second place to the right of the decimal point is the hundredths place because it is representative of the common fraction 1/ The decimal notation means 7 tens+3 ones+6 tenths+5 hundredths+2 thousandths. Next Slide

3.1 Place Value and Rounding 2 Example: This number is read as seventy-three and six hundred fifty-two thousandths. Writing a decimal in words Procedure: Writing a Decimal in Word Form Step 1. Write the whole number part in words (the number to the left of the decimal point). Step 2. Write the word “and” in place of the decimal point. Step 3. Write the decimal part in words as though it were a whole number without any commas followed by the name of the place value of the last digit. Example 1. Write the following in words. a) b) Answers: b) Seven and three hundred four ten-thousandths a) eighty-three thousandths Answers: b) ninety-one and thirty-six thousandths a) seventy-five hundredths Write the following in words. a) 0.75 b) Your Turn Problem #1

3.1 Place Value and Rounding 3 Changing a decimal written in words to decimal notation. When writing decimals in decimal notation, make sure the last digit is in the correct place value. Example 2: a) Five hundredths Words Answer: Decimal notation 0.05 The 5 must be in the hundredths place. b) forty-seven and twelve ten-thousandths The words before “and” give the whole number in front of the decimal point. 12 comes after the decimal point. We just need to make sure the last digit is in the ten-thousandths place by placing enough zeros before the Answer: Fifty-eight and nine hundred forty-three thousandths Write the following in words Your Turn Problem #2

3.1 Place Value and Rounding 4 Converting a Decimal to a Fraction or Mixed Number To convert a decimal to a fraction: 1. If the decimal has a whole number in front of the decimal point, this will also be the whole number part of the mixed number. 2.The digits to the right of the decimal point will be the numerator of the fraction. 3.The denominator will be the place value of the last digit. Example 3. Write the following as fractions. (Fractions should always be reduced if possible.) a) 0.25 b) Write the following as fractions. Your Turn Problem #3 a) 0.48 b) 29.4 Answer:

3.1 Place Value and Rounding 5 Rounding Decimals To round to a certain place: a) Locate the digit in the place value which is to be rounded. b) Consider the next digit to the right. c) If the digit to the right is 5 or greater, round up; add 1 to the specified place value. If the digit to the right is 4 or lower, round down; the specified place value remains the same. When rounding to a specific place, the last digit written should be the specified place value. Do not write any digits past that value. Examples 4. Round the following to the specified place value. a) (tenths) b) (hundredths) c) (hundredths) Answers a) 0.3 b) 5.45 c) Your Turn Problem #4 Round the following to the specified place value. a) (tenths) b) (hundredths) c) (thousandths) Answers a) 9.6 b) c) The End