Question

practice problems

1. express each number in scientific notation.

a. 700 c. 4,500,000 e. 0.0054 g. 0.000000076
b. 38,000 d. 685,000,000,000 f. 0.00000687 h. 0.0000000008

1. challenge express each quantity in regular notation along with its appropriate unit.

a. 3.60×10^5 s c. 5.060×10^3 km
b. 5.4×10^(-5) g/cm^3 d. 8.9×10^10 hz

Explanation:

Step1: Recall scientific - notation rule

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

Step2: Convert 700 to scientific notation

$700 = 7\times100=7\times10^{2}$

Step3: Convert 38000 to scientific notation

$38000 = 3.8\times10000 = 3.8\times10^{4}$

Step4: Convert 4500000 to scientific notation

$4500000=4.5\times1000000 = 4.5\times10^{6}$

Step5: Convert 685000000000 to scientific notation

$685000000000 = 6.85\times100000000000=6.85\times10^{11}$

Step6: Convert 0.0054 to scientific notation

$0.0054=\frac{5.4}{1000}=5.4\times10^{-3}$

Step7: Convert 0.00000687 to scientific notation

$0.00000687=\frac{6.87}{1000000}=6.87\times10^{-6}$

Step8: Convert 0.000000076 to scientific notation

$0.000000076=\frac{7.6}{100000000}=7.6\times10^{-8}$

Step9: Convert 0.00000000008 to scientific notation

$0.00000000008=\frac{8}{100000000000}=8\times10^{-11}$

Step10: Recall regular - notation rule

To convert from scientific notation $a\times10^{n}$ to regular notation, if $n>0$, move the decimal point $n$ places to the right; if $n < 0$, move the decimal point $|n|$ places to the left.

Step11: Convert $3.60\times10^{5}\text{s}$ to regular notation

$3.60\times10^{5}\text{s}=360000\text{s}$

Step12: Convert $5.4\times10^{-5}\text{g/cm}^3$ to regular notation

$5.4\times10^{-5}\text{g/cm}^3 = 0.000054\text{g/cm}^3$

Step13: Convert $5.060\times10^{3}\text{km}$ to regular notation

$5.060\times10^{3}\text{km}=5060\text{km}$

Step14: Convert $8.9\times10^{10}\text{Hz}$ to regular notation

$8.9\times10^{10}\text{Hz}=89000000000\text{Hz}$

Answer:

14.
a. $7\times10^{2}$
b. $3.8\times10^{4}$
c. $4.5\times10^{6}$
d. $6.85\times10^{11}$
e. $5.4\times10^{-3}$
f. $6.87\times10^{-6}$
g. $7.6\times10^{-8}$
h. $8\times10^{-11}$
15.
a. $360000\text{s}$
b. $0.000054\text{g/cm}^3$
c. $5060\text{km}$
d. $89000000000\text{Hz}$