Question

name: tyler calab
scientific measurements and calculations unit
express the following numbers using scientific notation:

1. 985
2. 463,000
3. 0.00549
4. 0.000019
5. 0.75
6. 3

express the following as whole numbers or decimals:

1. 5.6×10³
2. 9.05×10²
3. 8.3×10⁻⁴
4. 1.5×10⁻²
5. 4.6×10¹
6. 7.256×10⁰

perform the following calculations and express the answers in scientific notation.

1. (8.2×10³)+(3.0×10²)
2. (0.000074000)÷(0.0000060)
3. (-6.25×10³)×(6.5×10⁻⁶)
4. (3.25×10³)-(7.55×10²)
5. (0.0000567)(258,000,000,000)(0.9562)(987,654,000)
6. (0.000505032)÷(509,000,000,000,000)(0.05234)(583,583)

Explanation:

Step1: Recall scientific - notation rules

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

Step2: Convert 985

Move the decimal point 2 places to the left, so $985 = 9.85\times10^{2}$.

Step3: Convert 463000

Move the decimal point 5 places to the left, so $463000=4.63\times 10^{5}$.

Step4: Convert 0.00549

Move the decimal point 3 places to the right, so $0.00549 = 5.49\times10^{-3}$.

Step5: Convert 0.000019

Move the decimal point 5 places to the right, so $0.000019=1.9\times10^{-5}$.

Step6: Convert 0.75

Move the decimal point 1 place to the right, so $0.75 = 7.5\times10^{-1}$.

Step7: Convert 3

$3=3\times10^{0}$.

Step8: Convert $5.6\times10^{3}$ to decimal

Multiply 5.6 by 1000 (since the exponent of 10 is 3), so $5.6\times10^{3}=5600$.

Step9: Convert $9.05\times10^{2}$ to decimal

Multiply 9.05 by 100 (since the exponent of 10 is 2), so $9.05\times10^{2}=905$.

Step10: Convert $8.3\times10^{-4}$ to decimal

Divide 8.3 by 10000 (since the exponent of 10 is - 4), so $8.3\times10^{-4}=0.00083$.

Step11: Convert $1.5\times10^{-2}$ to decimal

Divide 1.5 by 100 (since the exponent of 10 is - 2), so $1.5\times10^{-2}=0.015$.

Step12: Convert $4.6\times10^{1}$ to decimal

Multiply 4.6 by 10 (since the exponent of 10 is 1), so $4.6\times10^{1}=46$.

Step13: Convert $7.256\times10^{0}$ to decimal

Since the exponent of 10 is 0, $7.256\times10^{0}=7.256$.

Step14: Calculate $(8.2\times10^{3})+(3.0\times10^{2})$

Rewrite $8.2\times10^{3}=8200$ and $3.0\times10^{2}=300$, then $8200 + 300=8500=8.5\times10^{3}$.

Step15: Calculate $(0.000074000)\div(0.0000060)$

Rewrite in scientific - notation: $7.4\times10^{-5}\div6.0\times10^{-6}=\frac{7.4}{6.0}\times10^{-5 + 6}\approx1.233\times10^{1}$.

Step16: Calculate $(-6.25\times10^{2})\times(6.5\times10^{-6})$

Multiply the coefficients: $(-6.25)\times(6.5)=-40.625$, and add the exponents: $2+( - 6)=-4$. So $-40.625\times10^{-4}=-4.0625\times10^{-3}$.

Step17: Calculate $(3.25\times10^{3})-(7.55\times10^{2})$

Rewrite $3.25\times10^{3}=3250$ and $7.55\times10^{2}=755$, then $3250-755 = 2495=2.495\times10^{3}$.

Step18: Calculate $(0.0000567)\times(258000000000)\times(0.9562)\times(987654000)$

Rewrite in scientific - notation: $5.67\times10^{-5}\times2.58\times10^{11}\times9.562\times10^{-1}\times9.87654\times10^{8}$.
Multiply the coefficients: $5.67\times2.58\times9.562\times9.87654\approx1381.57$.
Add the exponents: $-5 + 11-1 + 8=13$. So $1381.57\times10^{13}=1.38157\times10^{16}$.

Step19: Calculate $(0.000505032)\div(509000000000000)\times(0.05234)\times(583583)$

Rewrite in scientific - notation: $5.05032\times10^{-4}\div5.09\times10^{14}\times5.234\times10^{-2}\times5.83583\times10^{5}$.
$\frac{5.05032}{5.09}\times10^{-4-14}\times5.234\times5.83583\times10^{-2 + 5}\approx3.03066\times10^{-10}$.

Answer:

1. $9.85\times10^{2}$
2. $4.63\times10^{5}$
3. $5.49\times10^{-3}$
4. $1.9\times10^{-5}$
5. $7.5\times10^{-1}$
6. $3\times10^{0}$
7. 5600
8. 905
9. 0.00083
10. 0.015
11. 46
12. 7.256
13. $8.5\times10^{3}$
14. $1.233\times10^{1}$
15. $-4.0625\times10^{-3}$
16. $2.495\times10^{3}$
17. $1.38157\times10^{16}$
18. $3.03066\times10^{-10}$