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1. Introduction
Since 0.749 is a number less than one, n is a negative integer. In this case, n 1.
Combining the above two steps:
0.749 7.49 101
(b) Express 802.6 in scientific notation.
Solution: The decimal point must be moved two places to give N, a number between 1 and 10. In this case,
N 8.026
Since 802.6 is a number greater than one, n is a positive integer. In this case, n 2.
Combining the above two steps:
802.6 8.026 102
(c) Express 0.000000621 in scientific notation.
Solution: The decimal point must be moved seven places to give N, a number between 1 and 10. In this case,
N 6.21
Since 0.000000621 is a number less than one, n is a negative integer. In this case, n 7.
Combining the above two steps:
0.000000621 6.21 107
1.23 (a) 15,200 (b) 0.0000000778
1.24 (a) Express 3.256 105 in nonscientific notation.
For the above number expressed in scientific notation, n 5. To convert to nonscientific notation, the decimal point must be moved 5 places to the left.
3.256 105 0.00003256
(b) Express 6.03 106 in nonscientific notation.
For the above number expressed in scientific notation, n 6. The decimal place must be moved 6 places to the right to convert to nonscientific notation.
6.03 106 6,030,000
1.25 (a) 145.75 (2.3 101) 145.75 0.23 1.4598 102
(b)
(c) (7.0 103) (8.0 104) (7.0 103) (0.80 103) 6.2 103
(d) (1.0 104) (9.9 106) 9.9 1010
1.26 (a) Addition using scientific notation.
Strategy: Lets express scientific notation as N 10n. When adding numbers using scientific notation, we must write each quantity with the same exponent, n. We can then add the N parts of the numbers, keeping the exponent, n, the same.
Solution: Write each quantity with the same exponent, n.
Lets write 0.0095 in such a way that n 3. We have decreased 10n by 103, so we must increase N by 103. Move the decimal point 3 places to the right.
0.0095 9.5 103
Add the N parts of the numbers, keeping the exponent, n, the same.
9.5 103
8.5 103
18.0 103
The usual practice is to express N as a number between 1 and 10. Since we must decrease N by a factor of 10 to express N between 1 and 10 (1.8), we must increase 10n by a factor of 10. The exponent, n, is increased by 1 from 3 to 2.
18.0 103 1.8 102
(b) Division using scientific notation.
Strategy: Lets express scientific notation as N 10n. When dividing numbers using scientific notation, divide the N parts of the numbers in the usual way. To come up with the correct exponent, n, we subtract the exponents.
Solution: Make sure that all numbers are expressed in scientific notation.
653 6.53 102
Divide the N parts of the numbers in the usual way.
6.53 5.75 1.14
Subtract the exponents, n.
1.14 102 (8) 1.14 102 8 1.14 1010
(c) Subtraction using scientific notation.
Strategy: Lets express scientific notation as N 10n. When subtracting numbers using scientific notation, we must write each quantity with the same exponent, n. We can then subtract the N parts of the numbers, keeping the exponent, n, the same.
Solution: Write each quantity with the same exponent, n.
Lets write 850,000 in such a way that n 5. This means to move the decimal point five places to the left.
850,000 8.5 105
