Question

1. the mass of a paper clip is approximately 0.000525 kilograms. write this mass in scientific notation. 6.1×1e - 61
2. the distance from the earth to the sun is approximately 149,600,000 kilometers. write this distance in scientific notation.
3. write each number in standard notation. 7.8×10^9

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leqslant|a|\lt10$ and $n$ is an integer.

Step2: Convert 0.0000061 to scientific notation

Move the decimal point 6 places to the right to get $a = 6.1$ and since we moved the decimal point 6 places to the right, $n=-6$. So, $0.0000061 = 6.1\times10^{-6}$.

Step3: Convert 0.000525 to scientific notation

Move the decimal point 4 places to the right to get $a = 5.25$ and since we moved the decimal point 4 places to the right, $n = - 4$. So, $0.000525=5.25\times10^{-4}$.

Step4: Convert 149600000 to scientific notation

Move the decimal point 8 places to the left to get $a = 1.496$ and since we moved the decimal point 8 places to the left, $n = 8$. So, $149600000=1.496\times10^{8}$.

Step5: Convert $7.8\times10^{9}$ to standard notation

Since the exponent of 10 is 9, we move the decimal point 9 places to the right. So, $7.8\times10^{9}=7800000000$.

Answer:

1. $0.0000061 = 6.1\times10^{-6}$
2. $0.000525 = 5.25\times10^{-4}$
3. $149600000=1.496\times10^{8}$
4. $7.8\times10^{9}=7800000000$