Decimals

1. Decimals Line ‘em up or Count ‘em up

2. Unit Overview • By the end of this unit, you should be able to: • Represent decimals on a number line • Compare and order decimals • Round decimals • Use estimation to approximate an answer • Add, subtract, multiply, and divide decimals

3. Representing Decimals Decimals Numbers to the right of the decimal point are called decimals. Decimals represent numbers that have a value between to whole numbers.

4. Write a Decimal in Word Form • To write in word form, follow these steps: • Write the number to the left of the decimal. • Write “and” where the decimal point is. • Write the number that is to the right of the decimal point. • Write the place value of the digit furthest to the right. 1 7 5 4 2 17.542 Seventeen and five hundred forty-two thousandths

5. Write a Decimal in Word Form • To write in word form, follow these steps: • Write the number to the left of the decimal. • Write “and” where the decimal point is. • Write the number that is to the right of the decimal point. • Write the place value of the digit furthest to the right. 8 2 5 .825 eight hundred twenty-five thousandths

6. Write a Decimal in Word Form • To write in word form, follow these steps: • Write the number to the left of the decimal. • Write “and” where the decimal point is. • Write the number that is to the right of the decimal point. • Write the place value of the digit furthest to the right. 1 6 0 8 16.08 Seventeen and eight hundredths

7. Your Turn – Write these decimals in word form 1) 7.17 seven and seventeen hundredths 2) .068 sixty-eight thousandths 3) 9.0769 nine and seven hundred sixty-nine ten-thousandths • Tips • Only put hyphens (-) in the numbers 21 through 99 • Don’t use commas • Be sure of your place value

8. Write a decimal in standard form • Standard form is just the usual way we write numbers. Thirty-five and ninety-six ten-thousandths 3 5 0 0 9 6 .

9. Your Turn • Write three and eighty-five thousandths in standard form. • 3.085 • Write five tenths in standard form. • 0.5 • Write forty-one and sixty-two hundredths in standard form. • 41.62

10. Your turn – Challenge problem • Write this number in standard form: • one hundred two ten-thousandths • 0.0102 *Remember the word “AND”! one hundred AND two ten-thousandths= 100.0002 Totally different!

11. Write a decimal in Expanded form • Expanded form is a sum of the products of each digit and its place value. (???) • Basically, take each digit of the number and multiply it by its place value position. Then add all of those up. For example: • 32.14  Take the 3 times 10 because it is in the tens place. • + Take the 2 times 1 because it is in the ones place. • + Take the 1 times .1 because it is in the tenths place. • + Take the 4 times .01 because it is in the hundredths place. • Looks like this: (3 x 10) + (2 x 1) + ( 1 x .1) + (4 x .01) When you solve it, you get the original number: (3 x 10) + (2 x 1) + ( 1 x .1) + (4 x .01) (30) + (2) + (.1) + (.04) 32.14

12. Your Turn- Write this number in expanded form • Eleven and three tenths • 11.3

13. Your Turn- Write this number in expanded form • Two and five hundredths • 2.05

14. Your Turn- Write this number in expanded form • Thirty-four and sixteen hundredths • 34.16