Question

Write each of the following numbers in standard scientific notation. a. \(1 / 1033\) b. \(1 / 10^{5}\) c. \(1 / 10^{-7}\) d. \(1 / 0.0002\) e. \(1 / 3,093,000\) f. \(1 / 10^{-4}\) g. \(1 / 10^{9}\) h. \(1 / 0.000015\)

Short answer

a. \(9.68 \times 10^{-3}\) b. \(10^{-5}\) c. \(10^{7}\) d. \(5 \times 10^3\) e. \(3.235 \times 10^{-7}\) f. \(10^{4}\) g. \(10^{-9}\) h. \(6.67 \times 10^4\)

Step-by-step solution

a. \(1/1033\)

To write this number in scientific notation, we can divide 1 by 1033. When we do that, we get approximately 0.000968. To convert this to scientific notation, we can move the decimal point three places to the right, which will give us 9.68. Then, we multiply it by \(10^{-3}\) which gives us \(9.68 \times 10^{-3}\).

b. \(1/10^5\)

We know that \(1/10^5 = 10^{-5}\), so the scientific notation for this number is already given: \(10^{-5}\).

c. \(1/10^{-7}\)

When dividing by 10 raised to a negative power, we can change the exponent to a positive value. Therefore, \(1/10^{-7} = 10^{7}\).

d. \(1/0.0002\)

To rewrite this fraction in scientific notation, we can divide 1 by 0.0002, which gives us 5000. This can be written as \(5 \times 10^3\).

e. \(1/3,093,000\)

First, we convert the fraction to decimal: \(1/3,093,000 \approx 0.0000003235\). Now, we can rewrite this decimal in scientific notation: \(3.235 \times 10^{-7}\).

f. \(1/10^{-4}\)

Following the same procedure as the previous parts, we get: \(1/10^{-4} = 10^{4}\).

g. \(1/10^{9}\)

We already have this number in scientific notation: \(10^{-9}\).

h. \(1/0.000015\)

To rewrite this fraction in scientific notation, we can divide 1 by 0.000015, which gives us approximately 66666.67. This can be written as \(6.67 \times 10^4\). In conclusion, here are the numbers rewritten in standard scientific notation: a. \(9.68 \times 10^{-3}\) b. \(10^{-5}\) c. \(10^{7}\) d. \(5 \times 10^3\) e. \(3.235 \times 10^{-7}\) f. \(10^{4}\) g. \(10^{-9}\) h. \(6.67 \times 10^4\)