Decimals

1. Decimals Place Value, Word, Expanded and Standard Forms

2. What decimals are • Decimals show amounts between two consecutive counting numbers (3,4…) 0.45 is between 0 and 1 3.861 is between 3 and 4 25,196.8 is between 25,196 and 25,197

3. Decimal Word Names • Decimal word names always end in “-th” or “-ths” one tenth 0.1 four hundredths 0.04 seven and three tenths 7.3

4. Representing the decimal • The decimal is represented by the word “and” when writing and saying decimals in words. 2.1 = two and one tenth 4.5 = four and five tenths 17.61 = seventeen and sixty-one hundredths

5. How to write decimals numbers greater than one in word form • To write a number containing a whole number and decimal follow these steps: • Write the whole number in words • Write “and” • Write the numbers shown in the decimal • Write the last place a digit occupies in the decimal (the farthest right) 32.46 • thirty-two • and • forty-six • hundredths thirty-two and forty-six hundredths

6. To write decimals in expanded form • Write the place individually 5.306 =

7. To write decimals in expanded form • Write the place individually 5.306 = 5

8. To write decimals in expanded form • Write the place individually 5.306 = 5 + 0.3

9. To write decimals in expanded form • Write the place individually 5.306 = 5 + 0.3 + 0.006

10. To write decimals in expanded form • Write the place individually 5.306 = 5 + 0.3 + 0.006

11. To show the value of the decimal places in expanded form • Multiply the digit by the value of the corresponding place 5.306 =

12. To show the value of the decimal places in expanded form • Multiply the digit by the value of the corresponding place 5.306 = (5 x 1)

13. To show the value of the decimal places in expanded form • Multiply the digit by the value of the corresponding place 5.306 = (5 x 1) + (3 x 0.1)

14. To show the value of the decimal places in expanded form • Multiply the digit by the value of the corresponding place 5.306 = (5 x 1) + (3 x 0.1) + (6 x 0.001)

15. To show the value of the decimal places in expanded form • Multiply the digit by the value of the corresponding place 5.306 = (5 x 1) + (3 x 0.1) +(6 x 0.001)

16. To put a number in standard form • To put a number in standard (numeral) form from expanded form, just add all places together. 8 + 0.1 + 0.05 + 0.003

17. To put a number in standard form • To put a number in standard (numeral) form from expanded form, just add all places together. 8 0.1 0.05 0.003

18. To put a number in standard form • To put a number in standard (numeral) form from expanded form, just add all places together (be sure to line up your decimals). 8 0.1 0.05 + 0.003

19. To put a number in standard form • To put a number in standard (numeral) form from expanded form, just add all places together. 8 0.1 0.05 + 0.003 8.153

20. Now you try it • Standard form of one hundred thirty and three tenths • Expanded form of 0.56 • Word form of 0.234