Published on May 22, 2008
Slide 1: Decimals and Place Value Slide 2: The zero and the counting numbers (1,2,3,...) make up the set of whole numbers. But not every number is a whole number. Our decimal system lets us write numbers of all types and sizes, using a clever symbol called the decimal point. As you move right from the decimal point, each place value is divided by 10. Slide 3: In our number system, digits can be placed to the left and right of a decimal point, to indicate numbers greater than one or less than one. The decimal point helps us to keep track of where the "ones" place is. It's placed just to the right of the ones place. As we move right from the decimal point, each number place is divided by 10. Tens Ones Hundreds Tenths Hundredths Thousandths 5 2 1 4 3 6 and Slide 4: Watch the 9's for place value. Slide 5: Beyond the set of whole numbers, there are numbers that are less than one, but, greater than zero; they are known as fractional parts. The name lends itself well, as these numbers are parts, or fractions, of one whole. The rectangle, or whole, above has been divided into 10 equal parts, or tenths. Slide 6: The rectangle is 1 whole. If I place the rectangle with 10 equal parts over the whole I can see how 10 tenths = 1 whole. Slide 7: The hundredths place has 100 equal parts. Slide 8: The rectangle is 1 whole. If I place the rectangle with 100 equal parts over the whole I can see how 100 hundredths = 1 whole. Slide 9: What would six tenths look like? Slide 10: How many tenths are shaded in? 0.4 Slide 11: = = ____________ ____________ 0.8 0.4 Slide 12: What would thirty hundredths look like? Slide 13: How many hundredths are shaded in? 0.20 Slide 14: = ____________ 0.30 Slide 15: = ____________ 0.58 Slide 16: Decimals are equivalent, or = to decimals in other place values. one tenth = ten hundredths Use your decimal squares to find: one tenth = _____ thousandths 100 Slide 17: three tenths = ______ hundredths thirty Slide 18: seven tenths = ______ hundredths seventy Slide 19: Whole Number Portion The whole number portion of a decimal number are the digits to the left of the decimal place. Example: In the number 23.65, the whole number portion is 23. In the number 0.024, the whole number portion is 0 – There is nothing there! Slide 20: Which number is the whole number? 51.05 51 3.17 3 0.97 0 Slide 21: The whole number is to the left of the decimal. 70.006 Slide 22: Less Than A Whole Number Portion The less than a whole number (or fractional parts) portion of a decimal number are the digits to the right of the decimal place. Example: In the number 23.65, the less than a whole number portion is 65. In the number 0.024, the less than a whole number portion is 024. Slide 23: Which number is the less than the whole number? 34.77 77 2.09 09 0.1 1 Slide 24: The less than whole number is to the right of the decimal. 99.321 Slide 25: Hint #1: Remember to read the decimal point as "and" -- notice in the two numbers below what a difference that makes! 0.548 500.048 Slide 26: Hint #2: When writing a decimal number that is less than 1, a zero is normally used in the ones place: 0.526 not .526 A symbol for nothing--our zero--had to be invented. Zero "holds the place" for a particular value, when no other digit goes in that position. For example, the number “0.506" in words means no ones, 5 tenths, no hundredths and 6 thousandths. Without a symbol for nothing, our decimal number system wouldn't work. Slide 27: Writing Word Names For Decimals Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step. Write an and for the decimal point. Write out the number to the right of the decimal. Do not yet include the place value. Determine the place value of the last digit to the right of the decimal. Write the place value. Slide 28: Lets Practice 9.53 nine and fifty three hundredths 0.50 fifty hundredths Slide 29: On your own paper write the word names for each decimal. 500.006 0.71 2.60 0.8 Slide 30: 500.006 0.71 2.60 0.8 five hundred and six thousandths seventy one hundredths two and sixty hundredths eight tenths Slide 31: How would you write these numbers in decimal form? 321.7 three hundred twenty one and seven tenths 0.548 five hundred forty eight thousandths Slide 32: Writing Decimals in Fraction Form Let's try to figure out the fractional equivalent of the decimal .345. The 3 represents 3 tenths,the 4 represents 4 hundredthsthe 5 represents 5 thousandths So, we can write .345 = 3/10 + 4/100 + 5/1000. or Slide 33: Here's a shortcut for dealing with decimals: Instead of writing out .345 = 3/10 + 4/100 + 5/1000, then finding the common denominator, adding, and reducing, just think: 1. Ask yourself: What is the number? 345 2. Ask yourself: What is the place value? thousandths 3. Then place the 345 over the 1000. 345 1000 Slide 35: Lets Practice 0.53 53 100 0.3 3 10 0.801 81 1000 0.60 60 100 Slide 36: Ordering Decimals o o $3.50 $3.83 $3.45 $3.09 Write them in columns so the place values line up. Compare the digits in each column, starting at the left. Which pizza is cheapest? Slide 37: Log Book How many hundredths are in four tenths? Explain how you know and draw an example. Slide 38: There are forty hundredths in four tenths. I know this because one tenth is equal to 10 hundredths. So 10 + 10 + 10 + 10 = 0.40. If you lay them on top of each other they are the same.