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Decimal Help This PowerPoint will help you get ready for the test! Value of a Digit What is the digit in question worth? If it’s a three in the tenths place it’s worth three tenths or 0.3. Write the answer in numerical form. The value of the 9 in 7.895 is 0.09. The 9 is in the hundredths spot. 9 X 1/100 = 0.09 Practice: Find the value of the underlined numbers. 1. 32.893 2. 4.075 3. 63.867 4. 1.004 Value of a Digit Answers 1.32.893 = 0.003 2.4.075 = 0.07 3.63.867 = 0.8 4.1.004 = 0.004 Writing Decimals Using Expanded Form 22.17 in expanded form is 20 + 2 + 0.1 + 0.07 If you were to add those numbers up you would get 22.17 Find the value of each digit and write it one at a time with an addition sign between each one. Practice: Write the following numbers in regular expanded form. 5. 12.21 6. 0.135 7. 5.503 8. 0.018 Writing Decimals Using Expanded Form Answers 5. 6. 7. 8. 12.21 0.135 5.503 0.018 = = = = 10 + 2 + 0.2 + 0.01 0.1 + 0.03 + 0.005 5 + 0.5 + 0.003 0.01 + 0.008 Expanded Form Using Multiplication Now that you can do regular expanded form, let’s take it a step further. Take each number and decide what you need to multiply by the base number to make it using multiplication. 9.185 in expanded form multiplication is (9 X 1) + (1 X 1/10) + (8 X 1/100) + (5 X 1/1000) If you were to multiply what’s in each of the parenthesis and add the products together you would get a sum of 9.185. Practice: Write the following numbers in expanded form multiplication. 9. 62.783 10. 6.503 11. 0.185 12. 4.825 Expanded Form Using Multiplication Answers 9. 62.783 = (6 X 10) + (2 X 1) + (7 X 1/10) + (8 x 1/100) + (3 X 1/1000) 10. 6.503 = (6 X 1) + (5 X 1/10) + (3 X 1/1000) 11. 0.185 = (1 X 1/10) + (8 X 1/100) + (5 X 1/1000) 12. 4.825 = (4 X 1) + (8 X 1/10) + (2 X 1/100) + (5 X 1/1000) Rounding Decimals Round the number below to the nearest hundredths place. 3.241 The four is in the hundredths place. The one to the right says, “Leave it alone.” So, it stays a 4. Locate the number you’re asked to round to. You’ll have to know place value (location) for this. Then, look to the right. My students like to say, “Five and up bump it up. Four and below let it go.” That saying means if the number to the right is a five or higher you bump the number up one digit. If it’s a four or less, you don’t do anything to it. Leave it alone. The Answer is 3.240 or 3.24 All the numbers to the left of the hundredths place remain the same. The numbers to the right of the hundredths place become zeroes. Practice: Round the following numbers to the hundredths place. 13. 7.625 14. 12.333 15. 30.002 16. 51.066 Rounding Decimals Answers 13. 7.625 = 7.630 or 7.63 14. 12.333 = 12.330 or 12.33 15. 30.002 = 30.00 or 30 16. 51.066 = 51.070 or 51.07 Finding the Place Value of the Digit (Aka Location) In class we did a cheer. We said, “Ones, tenths, hundredths, thousandths.” 123 Practice: Name the location of the underlined digit. 17. 32.893 18. 75.618 19. 63.867 20. 29.912 The 2 is in the hundredths place. Finding the Place Value of the Digit (Aka Location) Answers 17. 18. 19. 20. 32.893 75.618 63.867 29.912 = = = = thousandths tenths hundredths hundredths Writing Numbers in Word Form The number 456 is four hundred fifty-six. The last spot is thousandths, so my last word is thousandths. 12.456 is twelve AND four hundred fifty-six thousandths Read the numbers to the left of the decimal how you would normally read them. When you see the decimal say, “AND.” Read the numbers to the right of the decimal as a group. Then say the last spot’s name. “Last spot last word!” Practice: Write the following numbers in word form. 21. 67.015 22. 522.04 23. 771.771 24. 84.97 Writing Numbers in Word Form Answers 21. 22. 23. 24. 67.015 = sixty-seven and fifteen thousandths 522.04 = five hundred twenty-two and four hundredths 771.771 = seven hundred seventy-one and seven hundred seventy-one thousandths 84.97 = eighty-four and ninety-seven hundredths Comparing Decimals 7.2 > 7.2 7.02 7.02 “The alligator eats the biggest number.” The number one tip I can give you is to line your decimals up then compare the numbers to determine which number is bigger or smaller. They both have sevens, but the tenths place is different. Two is bigger than zero, so 7.2 is the bigger number. Practice: Compare the two numbers using <, >, or =. 25. 0.21 0.211 26. 40.99 40.9 27. 6.22 6.220 28 9.44 9.4 Comparing Decimals Answers 25. 0.21 26. 40.99 27. 6.22 28. 9.44 < > = 0.211 > 9.4 40.9 6.220 Creating a Base Ten Block Display of a Decimal You need to be able to recreate a base ten block (10 X 10). 58 of the 100 blocks are shaded, so 0.58 is shaded. Vocabulary to Know Standard Form – A way to write numbers by using the digits 0 – 9, with each digit having a place value. E.g., 456 Expanded Form – A way to write numbers by showing the value of each digit. E.g., 832 = 800 + 30 + 2 Word Form – A way to write numbers in standard English. E.g., 4,829 = four thousand eight hundred twenty-nine Digit – Any one of the ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9 used to write numbers.