Question

Express each of the following numbers in scientific (exponential) notation. a. 529 b. 240,000,000 c. 301,000,000,000,000,000 d. 78,444 e. 0.0003442 f. 0.000000000902 g. 0.043 h. 0.0821

Short answer

a. \(5.29 \times 10^2\) b. \(2.4 \times 10^8\) c. \(3.01 \times 10^{17}\) d. \(7.8444 \times 10^4\) e. \(3.442 \times 10^{-4}\) f. \(9.02 \times 10^{-10}\) g. \(4.3 \times 10^{-2}\) h. \(8.21 \times 10^{-2}\)

Step-by-step solution

Find the value of a and b for scientific notation

The basic idea is to shift the decimal point of 529 until it's between 1 and 10, counting how many times the decimal is shifted to obtain the exponent value b. 529 can be written as 5.29 (decimal shifted two times to the left), thus a = 5.29 and b = 2.

Write the number in scientific notation

Now, we can write the number in the form of a × 10^b: \(529 = 5.29 \times 10^2\). #b. Expressing the number 240,000,000 in scientific notation#

Find the value of a and b for scientific notation

Shift the decimal point of 240,000,000 until it's between 1 and 10, counting how many times the decimal is shifted to obtain the exponent value b. 240,000,000 can be written as 2.4 (decimal shifted eight times to the left), thus a = 2.4 and b = 8.

Write the number in scientific notation

Now, we can write the number in the form of a × 10^b: \(240,000,000 = 2.4 \times 10^8\). And so on for the rest of the given numbers. #c. 301,000,000,000,000,000 in scientific notation: \(3.01 \times 10^{17}\) #d. 78,444 in scientific notation: \(7.8444 \times 10^4\) #e. 0.0003442 in scientific notation: \(3.442 \times 10^{-4}\) #f. 0.000000000902 in scientific notation: \(9.02 \times 10^{-10}\) #g. 0.043 in scientific notation: \(4.3 \times 10^{-2}\) #h. 0.0821 in scientific notation: \(8.21 \times 10^{-2}\)