IonlyneedpartD.Therestoftheinformationisonlyforreference Expressing numbers using powers of 10 (called scientific notation) has several advantages. First, you can easily tell how big a number is. If a number were written as 3180000031800000, you would have to count the digits to know its magnitude. However, 3.18×1073.18×107 is immediately seen to be somewhere in the neighborhood of 10 million (107107). In addition, the number of significant figures is just the number of digits in the factor preceding the exponent of 10. Since the number 3.18 has three significant figures, so does the entire number 3.18×1073.18×107. If you knew this number to five significant figures, then you would write 3.1800×1073.1800×107. Multiplying numbers in scientific notation When you multiply two numbers in scientific notation, you can multiply the two numbers preceding the powers of 10 and then add the exponents of the two powers of 10. For instance, (3.18×107)⋅(2.50×105)==(3.18⋅2.50)×(107⋅105)7.95×1012(3.18×107)⋅(2.50×105)=(3.18⋅2.50)×(107⋅105)=7.95×1012 Part A Part complete Compute (4.29×1015)⋅(1.55×10−4)(4.29×1015)⋅(1.55×10−4). Express your answer to three digits. View Available Hint(s) 6.65×1011 SubmitPrevious Answers Correct If you had been asked to multiply 4.29×10154.29×1015 times 3.00×10−43.00×10−4, you would have found (to three significant figures) 12.9×101112.9×1011. You should rewrite this in the more accepted form 1.29×10121.29×1012. (Notice that you must increase the exponent to balance moving the decimal point to the left.) Adding numbers in scientific notation To add numbers in scientific notation, you must proceed as follows: Be certain that the numbers have the same power of 10. Add the numbers preceding the ×× sign. This follows the distributive property in mathematics: 2.30×10−8+3.60×10−8=(2.30+3.60)×10−82.30×10−8+3.60×10−8=(2.30+3.60)×10−8 just as 2⋅5+4⋅5=(2+4)⋅52⋅5+4⋅5=(2+4)⋅5 Sometimes you will need to add two numbers that do not have the same power of 10, say 1.37×1061.37×106 and 2.21×1052.21×105. To add these, change one of the exponents so that the two exponents are equal. For instance, you can increase the smaller power of 10 and move the decimal point to the left. Each time that you increase the power of 10 by one, you must move the decimal point to the left once. For the two numbers considered here, you would have (rounding to three significant figures) 1.37×106+2.21×105===1.37×106+0.221×106(1.37+0.221)×1061.59×1061.37×106+2.21×105=1.37×106+0.221×106=(1.37+0.221)×106=1.59×106 Part B Part complete Compute 6.28×1013+9.30×10116.28×1013+9.30×1011. Express your answer to three digits. View Available Hint(s) 6.37×1013 SubmitPrevious Answers Correct Practice with a word problem Now practice the techniques you just learned for manipulating numbers written in scientific notation in the following set of word problems. Part C Part complete Suppose that a certain fortunate person has a net worth of $75.0 billion ($7.50×10107.50×1010). If her stock has a good year and gains $3.20 billion (3.20×1093.20×109) in value, what is her new net worth? Express your answer to three digits. View Available Hint(s) 7.82×1010 dollars SubmitPrevious Answers Correct Part D Suppose that this individual now decides to give one-eighth of a percent (0.125 %%) of her new net worth to charity. How many dollars are given to charity? Express your answer to three digits. View Available Hint(s) 1.25 dollars

IonlyneedpartD.Therestoftheinformationisonlyforreference Expressing numbers using powers of 10 (called scientific notation) has several advantages. First, you can easily tell how big a number is. If a number were written as 3180000031800000, you would have to count the digits to know its magnitude. However, 3.18×1073.18×107 is immediately seen to be somewhere in the neighborhood of 10 million (107107). In addition, the number of significant figures is just the number of digits in the factor preceding the exponent of 10. Since the number 3.18 has three significant figures, so does the entire number 3.18×1073.18×107. If you knew this number to five significant figures, then you would write 3.1800×1073.1800×107. Multiplying numbers in scientific notation When you multiply two numbers in scientific notation, you can multiply the two numbers preceding the powers of 10 and then add the exponents of the two powers of 10. For instance, (3.18×107)⋅(2.50×105)==(3.18⋅2.50)×(107⋅105)7.95×1012(3.18×107)⋅(2.50×105)=(3.18⋅2.50)×(107⋅105)=7.95×1012 Part A Part complete Compute (4.29×1015)⋅(1.55×10−4)(4.29×1015)⋅(1.55×10−4). Express your answer to three digits. View Available Hint(s) 6.65×1011 SubmitPrevious Answers Correct If you had been asked to multiply 4.29×10154.29×1015 times 3.00×10−43.00×10−4, you would have found (to three significant figures) 12.9×101112.9×1011. You should rewrite this in the more accepted form 1.29×10121.29×1012. (Notice that you must increase the exponent to balance moving the decimal point to the left.) Adding numbers in scientific notation To add numbers in scientific notation, you must proceed as follows: Be certain that the numbers have the same power of 10. Add the numbers preceding the ×× sign. This follows the distributive property in mathematics: 2.30×10−8+3.60×10−8=(2.30+3.60)×10−82.30×10−8+3.60×10−8=(2.30+3.60)×10−8 just as 2⋅5+4⋅5=(2+4)⋅52⋅5+4⋅5=(2+4)⋅5 Sometimes you will need to add two numbers that do not have the same power of 10, say 1.37×1061.37×106 and 2.21×1052.21×105. To add these, change one of the exponents so that the two exponents are equal. For instance, you can increase the smaller power of 10 and move the decimal point to the left. Each time that you increase the power of 10 by one, you must move the decimal point to the left once. For the two numbers considered here, you would have (rounding to three significant figures) 1.37×106+2.21×105===1.37×106+0.221×106(1.37+0.221)×1061.59×1061.37×106+2.21×105=1.37×106+0.221×106=(1.37+0.221)×106=1.59×106 Part B Part complete Compute 6.28×1013+9.30×10116.28×1013+9.30×1011. Express your answer to three digits. View Available Hint(s) 6.37×1013 SubmitPrevious Answers Correct Practice with a word problem Now practice the techniques you just learned for manipulating numbers written in scientific notation in the following set of word problems. Part C Part complete Suppose that a certain fortunate person has a net worth of $75.0 billion ($7.50×10107.50×1010). If her stock has a good year and gains $3.20 billion (3.20×1093.20×109) in value, what is her new net worth? Express your answer to three digits. View Available Hint(s) 7.82×1010 dollars SubmitPrevious Answers Correct Part D Suppose that this individual now decides to give one-eighth of a percent (0.125 %%) of her new net worth to charity. How many dollars are given to charity? Express your answer to three digits. View Available Hint(s) 1.25 dollars

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Multiplying numbers in scientific notation

When you multiply two numbers in scientific notation, you can multiply the two numbers preceding the powers of 10 and then add the exponents of the two powers of 10. For instance,

(3.18×107)⋅(2.50×105)==(3.18⋅2.50)×(107⋅105)7.95×1012(3.18×107)⋅(2.50×105)=(3.18⋅2.50)×(107⋅105)=7.95×1012

Part A

Part complete

Compute (4.29×1015)⋅(1.55×10−4)(4.29×1015)⋅(1.55×10−4).

Express your answer to three digits.

View Available Hint(s)

6.65×10¹¹

SubmitPrevious Answers

Correct

If you had been asked to multiply 4.29×10154.29×1015 times 3.00×10−43.00×10−4, you would have found (to three significant figures) 12.9×101112.9×1011. You should rewrite this in the more accepted form 1.29×10121.29×1012. (Notice that you must increase the exponent to balance moving the decimal point to the left.)

Adding numbers in scientific notation

To add numbers in scientific notation, you must proceed as follows:

Be certain that the numbers have the same power of 10.
Add the numbers preceding the ×× sign.

This follows the distributive property in mathematics:

2.30×10−8+3.60×10−8=(2.30+3.60)×10−82.30×10−8+3.60×10−8=(2.30+3.60)×10−8

just as

2⋅5+4⋅5=(2+4)⋅52⋅5+4⋅5=(2+4)⋅5

Sometimes you will need to add two numbers that do not have the same power of 10, say 1.37×1061.37×106 and 2.21×1052.21×105. To add these, change one of the exponents so that the two exponents are equal. For instance, you can increase the smaller power of 10 and move the decimal point to the left. Each time that you increase the power of 10 by one, you must move the decimal point to the left once. For the two numbers considered here, you would have (rounding to three significant figures)

1.37×106+2.21×105===1.37×106+0.221×106(1.37+0.221)×1061.59×1061.37×106+2.21×105=1.37×106+0.221×106=(1.37+0.221)×106=1.59×106

Part B

Part complete

Compute 6.28×1013+9.30×10116.28×1013+9.30×1011.

Express your answer to three digits.

View Available Hint(s)

6.37×10¹³

SubmitPrevious Answers

Correct

Practice with a word problem

Now practice the techniques you just learned for manipulating numbers written in scientific notation in the following set of word problems.

Part C

Part complete

Suppose that a certain fortunate person has a net worth of $75.0 billion ($7.50×10107.50×1010). If her stock has a good year and gains $3.20 billion (3.20×1093.20×109) in value, what is her new net worth?

Express your answer to three digits.

View Available Hint(s)

7.82×10¹⁰

dollars

SubmitPrevious Answers

Correct

Part D

Suppose that this individual now decides to give one-eighth of a percent (0.125 %%) of her new net worth to charity. How many dollars are given to charity?

Express your answer to three digits.

View Available Hint(s)

1.25

dollars

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