1. 1Confidential Our Lesson : Multiplying Decimals Multiplying Decimals

2. 2Confidential WARM UP 234 x 12 = 345.50 – 345.05 = Round 234 to the nearest tens Round 531. 58 to the nearest tenth

3. 3Confidential A decimal is a number that is written using the base ten place value system where a decimal point separates the ones’ and tenths’ digits. Each place value is 10 times the place value to it’s right. Lets review what we have learnt in the last lesson

4. 4Confidential Rules for rounding Decimals To round a decimal to a given place value, look at the digit in the place to the right If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. (round down) If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it. (round up) Let's Review what we have learnt in the last lesson

5. 5Confidential Find the place value you want and look at the digit just to the right of it. 5.834 To the nearest thousandth If that digit is less than 5, do not change the rounding digit but drop all digits to the right of it. 8 is greater than 5 If that digit is greater than or equal to five, add one to the rounding digit and drop all digits to the right of it so here we get6000 Review

6. 6Confidential Remember We can also round the decimals to their nearest Fractions in the same way Lets round 83. 461 to the nearest tenth place The place value number is 4 and number to its right is 6. 6 Is greater than 5 so We round the number to 83.5 83.4 6 1

7. 7Confidential Lets Get Started ! Today we will learn about Multiplying Decimals We are familiar with the multiplication of whole numbers. To multiply decimal numbers we first ignore the decimals and multiply as usual 35 x 21 = 735

8. 8Confidential Multiplying Decimals Starting on the right, multiply each digit in the top number by each digit in the bottom number just as you do with whole numbers Starting on the right, multiply each digit in the top number by each digit in the bottom number just as you do with whole numbers Now add the products. Now place the decimal point in the answer by starting at the right and moving the number of places equal to the sum of the decimal places in the factors (both numbers multiplied).

9. 9Confidential Let us understand it better with an example We find the product of 0.06 x 0.002 0.06 x 0.002 Ignore the decimal points and just multiply the two numbers Ignore the decimal points and just multiply the two numbers 6 × 2 = 12 6 × 2 = 12 Together 0.03 and 0.002 have five digits after decimal places. Therefore, start from the right and move left five places and then place the decimal We get 0.06 x 0.002 = 0. 0 0 0 1 2 We get 0.06 x 0.002 = 0. 0 0 0 1 2 5 4 3 2 1 -> Counting Decimal places12 345

10. 10Confidential Let us try another example Find the product of 1.251 x 2.3 1.251 x 2.3 1. 2 5 1 (3 decimal places) 1. 2 5 1 (3 decimal places) x 2. 3 (1 decimal place) x 2. 3 (1 decimal place) 3 7 5 3 3 7 5 3 2 5 0 2 2 5 0 2 2.8 7 7 3 2.8 7 7 3 The answer has 4 decimal places.

11. 11Confidential Solving another example Solving another example 1.5 1 1.5 1 x 6.2 x 6.2___________ 3 0 2 3 0 2 9 0 6 x 9 0 6 x__________ 9 3 6 2 9 3 6 2 Just count the numbers / places from right to left in both the numbers to be multiplied,and then add them and Insert the decimal after those many places. Multiply Decimals 12 3. \ \ \

12. 12Confidential Lets take another example Multiply 3.77 x (- 2.8) 3.7 7 3.7 7 x 2.8 x 2.8 _________ _________ 3 0 1 6 3 0 1 6 7 5 4 7 5 4 _________ _________ -10.5 5 6 -10.5 5 6 __________ __________ Note the negative sign. The rules of Multiplying remain the same

13. 13Confidential Rules of Multiplying Let us recap these rules When we multiply two numbers with Same sign we get + And with Different sign we get -

14. 14Confidential If we multiply any decimal number with 10, 100, 1000 etc The decimal point shifts to the right 2.367 x 100 The decimal point will shift to the right equal to the number of zeros with 1 In 100 there are 2 zeros so the decimal will shift two places to the right 2.367 x 100 = 236.7 Multiplying with 10, 100, 100

15. 15Confidential Lets try another example of this 2.3 x 1000 = ? There are 3 zeros with one in 1000 So the decimal point will shift 3 places 12.3856 x 1000 = 12 3 8 5 6.

16. 16Confidential You try some ! 0.002 x 15.04 = 0.00404 x 2 = 0.1 x.02 = 0.1 x.02 = 3215.0 x 0.0002 = 687.2 x 10 =

17. 17Confidential BREAK TIME

18. 18Confidential LETS PLAY A GAME Click Here to Play

19. 19Confidential Zack wants to purchase 15 chocolates and 50 candies. If each chocolate costs $2.3 and candy cost $0.52. How much money does Zack need to purchase these wares rounded to the nearest dollar.

20. 20Confidential 100 kg of Rice was distributed to poor people during a community service. If each Kg costs $ 1.50 and each person was given 5 Kg of rice. How much amount was spent on each person? How many people got the rice?

21. 21Confidential Each apple costs $1.5. Each boy is given 4 apples. How many apples are required to feed 20 boys. What is the total cost incurred?

22. 22Confidential Assessment 1.0.4 x.6 2.0.9 x 0.91 3.0.8 x 3 4.0.7 x 0.01 5.Evaluate the expression 1.12pq when p =2.29 and q=0.034 6.Evaluate the expression 12.54 x 0.023 x 11

23. 23Confidential Assessment 7.Evaluate the expression 10.72 + 6.8 x 9.08 8.Evaluate the expression 0.34 x (7.4 – 3.19) 9.Evaluate the expression 18.62 – 1.04 x 12.7 10.Halley’s comet takes about 23.06 times longer than Encke’s Comet to orbit the Sun. Encke’s Comet takes about 3.3 years. About how long does Halley’s Comet take to orbit the Sun? Round to the nearest tenth.

24. 24Confidential Lets Review what we have learnt in this lesson To multiply decimal numbers Ignore the decimal points Align them and multiply the numbers as whole numbers like this : 5 8 8.0 9 x 257.2 5 8 8.0 9 x 257.2 58809 58809 x 2572 x 2572 ______________ ______________ 15125648 15125648

25. 25Confidential In the final product count how many decimal places are there on the right side of the decimal points in the two numbers that are multiplied Now add them and place the decimal point in your answer so that there are those many numbers on the right. 5 8 8. 09 2 decimal places x 2 5 7. 2 1 decimal place ______________ 151256 748 Remember Always count from right side to put the decimal 3 2 1.

26. 26Confidential The decimal point will shift to the right equal to the number of zeros with 1 If we multiply any decimal number with 10, 100, 1000 etc 32.76 x 10 = 3 2 7 6.

27. 27Confidential Be sure to practice what you have learned. You had a Great Lesson Today