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Math 009 Unit 4 Lesson 1

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**Obj: To write decimals in words**

thousandths ten-thousandths and tenths hundredths ones hundreds tens 1 5 1 5 7 15.157 Fifteen and one hundred fifty-seven thousandths

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**Obj: To write decimals in words**

thousandths ten-thousandths and tenths hundredths ones hundreds tens 3 6 1 7 Three hundred six and seventeen ten-thousandths

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**Obj: To write words as decimals**

thousandths ten-thousandths and tenths hundredths ones hundreds tens 5 3 8 Five and thirty-eight hundredths Answer: 5.38

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**Obj: To write words as decimals**

thousandths ten-thousandths and tenths hundredths ones hundreds tens 1 9 4 Nineteen and four thousandths Answer: 19.004

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**Obj: To write words as decimals**

thousandths ten-thousandths and tenths hundredths ones hundreds tens 7 1 Seventy-one ten-thousandths Answer: 0.0071

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**Naming place values: Name the place value of the digit 7 56.03789**

thousandths hundred-thousandths tenths

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**Ordering decimal numbers**

Place the correct symbol between the two numbers Line up the decimals < 7.6005 7.605 Write the following numbers in order from smallest to largest 0.24, 0.024, 0.204, 0.24 0.024 0.204 0.0024 0.024 0.0024 Answer: 0.24 0.204 0.0024, 0.024, 0.204, 0.24

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**Obj: To round a decimal to a given place value.**

Round to the nearest hundredth 4.35 Round to the nearest ten-thousandth 4.3493

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**Obj: To round a decimal to a given place value.**

Round to the nearest tenth 4.3 Round to the nearest hundredth 15.05 Round to the nearest tenth 15.1

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**Operations on decimals**

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**Obj: To add decimals without a calculator**

Write the numbers so that the decimals points are on a vertical line add the columns just as you would with whole numbers Example: Find the sum of 42.3, and 1 1 1 + 9 0.2759 .2759 759 59 Answer:

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**Obj: To subtract decimals without a calculator**

Write the numbers so that the decimals points are on a vertical line subtract the columns just as you would with whole numbers Example: Subtract and 7.96 14 8 9 39.047 – 7.96 Answer:

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**Find the following sums or differences**

= – (-8.3) = = 9.39 – (-3.82) – = – = 4. How much greater is -31 than ? -31 – (-62.09) = =

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**Obj: To solve application problems involving decimals**

Find the missing length on the shaft 8.6 cm 2.77 cm ? 3.2 cm Solution: = 5.97 missing length = 8.6 – 5.97 missing length = 2.63 cm

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**Obj: To solve application problems involving decimals**

Grace owned shares of a mutual fund on January 1. On December 31 of the same year she noticed that her shares had increased by shares. What was her new total at the end of that year? Solution: New Total = = shares

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**Estimate by rounding; then find the exact answer**

6.272 – 1.848 Estimation: 6 – 2 = 4 Exact answer: 6.272 – = Evaluate x – y when x = and y = x – y = 6.029 – (-4.708) = =

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**Obj: To multiply decimals without a calculator**

multiply the numbers as if they were whole numbers the number of decimal places in the answer is the sum of the decimal places in the factors Multiply: x Total decimal places in the factors is 9 x 602 430 Total decimal places in the answer is 9 00000 4902 ^ Answer:

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**Obj: To divide decimals without a calculator**

Round your answer to the nearest tenth 5 9 6 1 7.06 420.9 706 42090. 00 ^ ^ 3530 Answer 59.6 679 6354 436 423 6 12 4 7 06

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**Do the following multiplications and divisions**

(0.72)(-3.7) -5.2(-0.8) (10,000) ¸ (-0.4) 58.37 ¸ 1000 = = = = =

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**Do the following multiplications and divisions**

Round answers to the nearest hundredth (5.78)(-3.799) -(18.47)(2.003) 8.57 ¸ ¸ (-3.14) = » = » = » = »

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**Obj: To multiply decimals by powers of 10**

move the decimal point to the right the same number of places as the number of zeros in the power of 10 Multiply: x 1000 .4207 x 1000 = 4207 = ^ Multiply: x 10,000 63.75 x 10,000 = 6375 00 = 637,500 ^

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**Obj: To multiply decimals by powers of 10**

if the power of 10 is written in exponent form move the decimal point to the right the same number of places as the power of 10 Multiply: x 103 x 103 = = ^ Multiply: x 105 4.68 x 105 = 468 000 = 468,000 ^

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**Obj: To divide decimals by powers of 10**

move the decimal in the dividend to the left the same number of places as the power of 10 (same number of places as the number of zeros) Divide: ¸ 103 58.3 ¸ 103 = = ^ Divide: ¸ 100 0.625 ¸ 100 = = ^

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**8 4 8. 68 4. 1666… 4.16 Obj: To convert fractions to decimals**

divide the numerator by the denominator place a bar over repeating digits round the decimal answer if necessary Convert to a decimal: 3 8 = 0.375 17 25 8 8. 68 = 1 6 4 4. 1666… 4.16 = =

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**Certain conversions from fractions to decimals should be memorized**

Obj: To convert fractions to decimals Certain conversions from fractions to decimals should be memorized 14 = 0.25 13 = 0.333… = 0.3 12 = 0.5 23 = 0.666… = 0.6 34 = 0.75

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**5 5 Obj: Convert decimals to fractions Convert fractions 35 7 = 0.35 =**

remove the decimal point for a denominator use a power of ten that corresponds to the decimal places in the original number reduce the fraction Convert fractions 35 7 = 0.35 = 100 20 275 11 = 0.275 = 1000 40 5 5 19 25 5.76 = =

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**> < Obj: Compare a decimal and a fraction 3 8 4.509 4 0.32 0.32**

change the fraction to a decimal compare the decimals Place the correct symbol, > or <, between the numbers 3 8 > 12 < 4.509 4 0.32 0.32 0.375 4.509 4.5 0.32 4.509 0.375 4.5 00

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**Checking a solution to an equation**

Is a solution for 6.4 = x ? 6.4 = x 6.4 5.2 + (-1.2) 4 No , is not a solution for the equation

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**Checking a solution to an equation**

Is a solution for -9x = ? -9x = -9(-3.6) 32.4 32.4 Yes , is a solution for the equation

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