Name: Class: Date: Class Notes - Division Lesson Six. 1) Bring the decimal point straight up to the roof of the division symbol.

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1 Name: Class: Date: Goals:11 1) Divide a Decimal by a Whole Number 2) Multiply and Divide by Powers of Ten 3) Divide by Decimals To divide a decimal by a whole number: Class Notes - Division Lesson Six 1) Bring the decimal point straight up to the roof of the division symbol. 2) Divide as though both numbers were whole numbers, adding zeroes to your dividend when necessary to carry out your answer (no remainders!). 3) Check if answer is reasonable (compatible numbers). For Example: Step 1: Bring the decimal point straight up to the roof of the division symbol. Classwork Step 2: Divide as though both numbers were whole numbers, adding zeroes to your dividend when necessary to carry out your answer (no remainders!). Remember, it is important to keep both digits and decimal points lined up when dividing!

2 Step 3: Check if answer is reasonable (compatible numbers). When we divided , our quotient (answer), was To check if this answer is reasonable, use compatible numbers! Since 8 is close to 10, and 9.92 is close to 10, round the dividend and the divisor to = is close to 1, so we know our answer is reasonable! Your Turn! Find the quotient. 1) ) ) 7 23 (round your answer to the nearest thousandth) Don t stop after the quotient has only three decimal places. If you do, you won t know whether to round up or down.

3 Goal 2: Multiply and Divide by Powers of Ten Vocabulary! factor: power: base: exponent: Astronomy A light-year is the distance light travels in one year. Astronomers estimate that the distance across the Virgo Spiral Galaxy is about 100,000 light-years. You can write 100,000 as a product. 100,000 = 10 x 10 x 10 x 10 x 10 This product has five factors of 10. When whole numbers other than zero are multiplied together, each number is a factor of the product. To write a product that has a repeated factor, you can use a power. The base of a power is the repeated factor and the exponent is the number of times the factor is repeated. base exponent 6 3 = 6 x 6 x 6 power there are three factors

4 Example 1: Use the distance across the Virgo Spiral Galaxy given above. Write the distance as a power. 10 x 10 x 10 x 10 x 10 = 10 5 There are 5 factors. Answer: The distance across the galaxy is about 105 light-years. Your Turn! Write the product as a power. 1) 8 x 8 x 8 2) 20 x 20 3) 11 x 11 x 11 x 11 x 11 4) 15 x 15 x 15 Reading Powers: When powers have an exponent of 2, the base is squared. When powers have an exponent of 3, the base is cubed. 3 2 is read 3 to the second power, or 3 squared. 4 3 is read 4 to the third power, or 4 cubed. 2 5 is read 2 to the fifth power. Example 2: Find the value of five cubed. 5 3 = 5 x 5 x 5 Write 5 as a factor three times. = 125 Multiply. Your Turn! Find the value of the power. 5) ) 5 4 7) 3 to the sixth power 8) 6 3

5 What happens when you multiply by a power of ten? Complete the table below. Whole Number Powers of Ten Decimal Powers of Ten 10 x 8.3 = 0.1 x 8.3 = 100 x 8.3 = 0.01 x 8.3 = 1000 x 8.3 = x 8.3 = 10,000 x 8.3 = x 8.3 = When you multiply by a whole number power of 10, the decimal point moves one place to the: for each zero in the whole number power of 10. When you multiply by a decimal power of 10, the decimal point moves one place to the: for each decimal place in the decimal power of 10. Examples: Find the product using mental math. 1) 0.05 x 1000 (think: the decimal point moves 3 places to the right) = 50 2) x (think: the decimal point moves 4 places to the left) = Your Turn! 3) 6.07 x 1000 = 5) x 0.1 = 4) x 0.01 = 6) 0.7 x 10,000 =

6 What happens when you divide by a power of 10? Complete the table below. Whole Number Powers of Ten Decimal Powers of Ten = = = = = = 35 10,000 = = When you divide by a whole number power of 10, the decimal point moves one place to the: for each zero in the whole number power of 10. When you divide by a decimal power of 10, the decimal point moves one place to the: for each decimal place in the decimal power of 10. Examples: Find the quotient using mental math. 1) (think: the decimal point moves 1 places to the left) = ) (think: the decimal point moves 2 places to the right) = 50,830 Your Turn! 3) = 5) = 4) = 6) =

7 Goal 3: Divide by Decimals. When you divide by a decimal, multiply both the divisor and the dividend by a power of ten that will make the divisor a whole number. For example: Multiply 2.5 and 3.75 by Multiply 0.15 and 3 by Step by Step: 1) Move the decimal point in the divisor to the right end, counting the hops as you go. 2) Move the decimal point in the dividend to the right the same number of hops, adding zeroes for place value when necessary. 3) Bring the decimal point straight up to the roof of the division symbol. 4) Divide, adding zeroes to your dividend when necessary to carry out your answer. Examples: Find the quotient. 1) )

8 Your turn! Round to the nearest tenth. 3) ) ) ) ) You paid $10.17 for 3.4 pounds of dried fruit. What was the cost per pound? Answer sentence: