Question

6 the approximate speed of light is 1,080,000,000 kilometers per hour. write this speed in scientific notation.
write each number in standard notation.
7 6.8 x 10^7
8 3.07 x 10^4
9 4.192 x 10^8
10 4 x 10^5
11 the diameter of jupiter is approximately 8.69 x 10^4 miles. write this distance in standard notation.
12 the population of china, in 2017, was approximately 1.386 x 10^9. write this number in standard notation.

Explanation:

Step1: Recall scientific - notation rule

Scientific notation is of the form $a\times10^{n}$, where $1\leq a < 10$ and $n$ is an integer. To convert from scientific notation to standard notation, if $n>0$, we move the decimal point $n$ places to the right. To convert from standard notation to scientific notation, we move the decimal point to get a number $a$ between 1 and 10 and count the number of places moved as $n$.

Step2: Convert 33,900,000 to scientific notation

Move the decimal point 7 places to the left to get $a = 3.39$. So, $33900000=3.39\times 10^{7}$.

Step3: Convert 1,080,000,000 to scientific notation

Move the decimal point 9 places to the left to get $a = 1.08$. So, $1080000000 = 1.08\times 10^{9}$.

Step4: Convert $6.8\times 10^{7}$ to standard notation

Move the decimal point 7 places to the right. $6.8\times 10^{7}=68000000$.

Step5: Convert $3.07\times 10^{4}$ to standard notation

Move the decimal point 4 places to the right. $3.07\times 10^{4}=30700$.

Step6: Convert $4.192\times 10^{8}$ to standard notation

Move the decimal point 8 places to the right. $4.192\times 10^{8}=419200000$.

Step7: Convert $4\times 10^{5}$ to standard notation

Move the decimal point 5 places to the right. $4\times 10^{5}=400000$.

Step8: Convert $8.69\times 10^{4}$ to standard notation

Move the decimal point 4 places to the right. $8.69\times 10^{4}=86900$.

Step9: Convert $1.386\times 10^{9}$ to standard notation

Move the decimal point 9 places to the right. $1.386\times 10^{9}=1386000000$.

Answer:

• 33,900,000 in scientific notation: $3.39\times 10^{7}$
• 1,080,000,000 in scientific notation: $1.08\times 10^{9}$
• $6.8\times 10^{7}$ in standard notation: 68000000
• $3.07\times 10^{4}$ in standard notation: 30700
• $4.192\times 10^{8}$ in standard notation: 419200000
• $4\times 10^{5}$ in standard notation: 400000
• 8.69×10⁴ miles in standard notation: 86900
• 1.386×10⁹ in standard notation: 1386000000