QuestionAugust 24, 2025

52. Express the following in exponential (scientific) notation: (a) 8,000,000 (b) 0.000075 (c) 23,600 ,000,000 (d) 37,000 (e) 6492 (f) 0.000000028

52. Express the following in exponential (scientific) notation: (a) 8,000,000 (b) 0.000075 (c) 23,600 ,000,000 (d) 37,000 (e) 6492 (f) 0.000000028
52. Express the following in exponential (scientific) notation: (a) 8,000,000 (b) 0.000075 (c) 23,600 ,000,000 (d) 37,000 (e) 6492 (f) 0.000000028

Solution
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Answer

(a) 8 \times 10^6, (b) 7.5 \times 10^{-5}, (c) 2.36 \times 10^{10}, (d) 3.7 \times 10^4, (e) 6.492 \times 10^3, (f) 2.8 \times 10^{-8} Explanation 1. Convert to Scientific Notation Move the decimal point in each number so that there is one non-zero digit to its left. Count the number of places moved as the exponent of 10. (a) ( 8,000,000 ): Move 6 places left. 8 \times 10^6 (b) 0.000075: Move 5 places right. 7.5 \times 10^{-5} (c) ( 23,600,000,000 ): Move 10 places left. 2.36 \times 10^{10} (d) 37,000: Move 4 places left. 3.7 \times 10^4 (e) 6492: Move 3 places left. 6.492 \times 10^3 (f) 0.000000028: Move 8 places right. 2.8 \times 10^{-8}

Explanation

1. Convert to Scientific Notation<br /> Move the decimal point in each number so that there is one non-zero digit to its left. Count the number of places moved as the exponent of 10.<br /><br />(a) ( 8,000,000 ): Move 6 places left. $8 \times 10^6$ <br />(b) 0.000075: Move 5 places right. $7.5 \times 10^{-5}$ <br />(c) ( 23,600,000,000 ): Move 10 places left. $2.36 \times 10^{10}$ <br />(d) 37,000: Move 4 places left. $3.7 \times 10^4$ <br />(e) 6492: Move 3 places left. $6.492 \times 10^3$ <br />(f) 0.000000028: Move 8 places right. $2.8 \times 10^{-8}$
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