Question

physical science
scientific notation ws1
convert the following numbers to scientific notation.

1. 9,650,000
2. 0.000012
3. 0.000023
4. 45,030,000,000
5. 0.001

convert the following to \standard numbers\.

1. 9.4 x 10^4
2. 1.46 x 10^3
3. 4.2 e -5 (this is how most calculators represent scientific notation)
4. 6.02 x 10^23

perform the following calculation without calculator.

1. (2.0 x 10^3)(3.0 x 10^4)
2. 7.5 x 10^-3 + 1.5 x 10^-2
3. 12 x 10^4 / 4.0 x 10^2

Explanation:

Step1: Recall scientific - notation rules

Scientific notation is of the form $a\times10^{n}$, where $1\leq a<10$ and $n$ is an integer.

Step2: Convert 9,650,000 to scientific notation

Move the decimal 6 places to the left. So, $9650000 = 9.65\times10^{6}$.

Step3: Convert 0.000012 to scientific notation

Move the decimal 5 places to the right. So, $0.000012=1.2\times10^{- 5}$.

Step4: Convert 0.000023 to scientific notation

Move the decimal 5 places to the right. So, $0.000023 = 2.3\times10^{-5}$.

Step5: Convert 45,030,000,000 to scientific notation

Move the decimal 10 places to the left. So, $45030000000=4.503\times10^{10}$.

Step6: Convert 0.001 to scientific notation

Move the decimal 3 places to the right. So, $0.001 = 1\times10^{-3}$.

Step7: Convert $9.4\times10^{4}$ to standard number

Move the decimal 4 places to the right. So, $9.4\times10^{4}=94000$.

Step8: Convert $1.46\times10^{3}$ to standard number

Move the decimal 3 places to the right. So, $1.46\times10^{3}=1460$.

Step9: Convert $4.2E - 5$ to standard number

$4.2E - 5$ means $4.2\times10^{-5}$. Move the decimal 5 places to the left. So, $4.2\times10^{-5}=0.000042$.

Step10: Convert $6.02\times10^{23}$ to standard number

Move the decimal 23 places to the right. So, $6.02\times10^{23}=602000000000000000000000$.

Step11: Calculate $(2.0\times10^{3})(3.0\times10^{4})$

Multiply the coefficients and add the exponents. $(2.0\times3.0)\times10^{3 + 4}=6.0\times10^{7}$.

Step12: Calculate $7.5\times10^{-3}+1.5\times10^{-2}$

Rewrite $1.5\times10^{-2}$ as $15\times10^{-3}$. Then $7.5\times10^{-3}+15\times10^{-3}=(7.5 + 15)\times10^{-3}=22.5\times10^{-3}=2.25\times10^{-2}$.

Step13: Calculate $12\times10^{4}\div4.0\times10^{2}$

Divide the coefficients and subtract the exponents. $(12\div4.0)\times10^{4 - 2}=3\times10^{2}$.

Answer:

1. $9.65\times10^{6}$
2. $1.2\times10^{-5}$
3. $2.3\times10^{-5}$
4. $4.503\times10^{10}$
5. $1\times10^{-3}$
6. $94000$
7. $1460$
8. $0.000042$
9. $602000000000000000000000$
10. $6.0\times10^{7}$
11. $2.25\times10^{-2}$
12. $3\times10^{2}$