Question

1. scientific notation review: put in scientific notation: a) 0.000003845 b) 45,030,000 c) 450,000,000 d).0000000098010 e) 506700 put in regular notation: a) 5.206 x 10^4 b) 2.320 x 10^ - 4 c) 5.20300 x 10^ - 7 d) 7.406 x 10^8 perform the following calculations and round according to the appropriate rule. note: you may have to put into scientific notation in order to show correct number of significant figures calculator answer rounded answer 5) 4.60 + 3 6) 0.008 + 0.05 7) 200 - 87.3 8) 67.5 - 0.009 9) 13.7 x 2.5 10) 200 x 3.58 11) 5000 / 55 12) 5003 / 3.781 13) (2.58 x 10^ - 3) x (6.1 x 10^5) 14) round each measurement to three significant figures. note: you may have to put into scientific notation to show 3 significant figures a) 0.01552 m b) 9009 m c) 1.7777 x 10^3 m d) 629.55 m e) 9459 m f) 39,952 g 15) calculate the volume of a warehouse that has inside dimensions of 22.4 m by 11.3 m by 5.2 m. (volume = l x w x h) use the correct significant digits in your answer.

Explanation:

Step1: Convert to scientific/regular notation and perform calculations

4. Scientific Notation Review

a) Scientific to Regular Notation

• Given $5.206\times 10^{4}$, move the decimal point 4 places to the right. So it is $52060$.

b) Scientific to Regular Notation

• Given $2.320\times 10^{-4}$, move the decimal point 4 places to the left. So it is $0.0002320$.

c) Scientific to Regular Notation

• Given $5.20300\times 10^{-7}$, move the decimal point 7 places to the left. So it is $0.000000520300$.

d) Scientific to Regular Notation

• Given $7.406\times 10^{8}$, move the decimal point 8 places to the right. So it is $740600000$.

a) Regular to Scientific Notation

• $0.000003845 = 3.845\times 10^{-6}$

b) Regular to Scientific Notation

• $45030000 = 4.503\times 10^{7}$

c) Regular to Scientific Notation

• $450000000 = 4.5\times 10^{8}$

d) Regular to Scientific Notation

• $0.000000098010=9.8010\times 10^{-8}$

e) Regular to Scientific Notation

• $506700 = 5.067\times 10^{5}$

5 - 13. Calculations and Rounding

5) $4.60 + 3$

• Calculator Answer: $7.60$
• Rounded Answer: $7.6$ (since 3 has no decimal - places, we round to the same precision as 3)

6) $0.008+0.05$

• Calculator Answer: $0.058$
• Rounded Answer: $0.058$ (both numbers have three significant - figures in the decimal part)

7) $200 - 87.3$

• Calculator Answer: $112.7$
• Rounded Answer: $113$ (200 has no decimal - places)

8) $67.5−0.009$

• Calculator Answer: $67.491$
• Rounded Answer: $67.5$ (67.5 has one decimal - place)

9) $13.7\times2.5$

• Calculator Answer: $34.25$
• Rounded Answer: $34$ (2.5 has two significant - figures)

10) $200\times3.58$

• Calculator Answer: $716$
• Rounded Answer: $720$ (200 has one significant - figure)

11) $5000\div55$

• Calculator Answer: $\frac{5000}{55}\approx90.90909\cdots$
• Rounded Answer: $91$ (55 has two significant - figures)

12) $5003\div3.781$

• Calculator Answer: $\frac{5003}{3.781}\approx1323.2$
• Rounded Answer: $1320$ (3.781 has four significant - figures)

13) $(2.58\times 10^{-3})\times(6.1\times 10^{5})$

• First, multiply the coefficients: $2.58\times6.1 = 15.738$.
• Then, add the exponents: $- 3+5 = 2$.
• So the result is $15.738\times 10^{2}=1.5738\times 10^{3}$.
• Rounded Answer: $1.57\times 10^{3}$ (6.1 has two significant - figures)

14. Rounding to three significant figures

a) $0.01552m$

• Rounded to three significant figures is $0.0155m$ or $1.55\times 10^{-2}m$.

b) $9009m$

• Rounded to three significant figures is $9010m$ or $9.01\times 10^{3}m$.

c) $1.7777\times 10^{3}m$

• Rounded to three significant figures is $1.78\times 10^{3}m$.

d) $629.55m$

• Rounded to three significant figures is $630m$ or $6.30\times 10^{2}m$.

e) $9459m$

• Rounded to three significant figures is $9460m$ or $9.46\times 10^{3}m$.

f) $39952g$

• Rounded to three significant figures is $40000g$ or $4.00\times 10^{4}g$.

15. Calculate the volume of the warehouse

• Volume $V=l\times w\times h$, where $l = 22.4m$, $w = 11.3m$, $h = 5.2m$.
• $V=22.4\times11.3\times5.2$
• $V = 22.4\times(11.3\times5.2)=22.4\times58.76 = 1316.224m^{3}$
• Rounded to the appropriate number of significant - figures (5.2 has two significant - figures), the volume is $1300m^{3}$ or $1.3\times 10^{3}m^{3}$.

Answer:

4. Scientific Notation Review

a) $52060$

b) $0.0002320$

c) $0.000000520300$

d) $740600000$

a) $3.845\times 10^{-6}$

b) $4.503\times 10^{7}$

c) $4.5\times 10^{8}$

d) $9.8010\times 10^{-8}$

e) $5.067\times 10^{5}$

5 - 13. Calculations and Rounding

5) Calculator Answer: $7.60$, Rounded Answer: $7.6$

6) Calculator Answer: $0.058$, Rounded Answer: $0.058$

7) Calculator Answer: $112.7$, Rounded Answer: $113$

8) Calculator Answer: $67.491$, Rounded Answer: $67.5$

9) Calculator Answer: $34.25$, Rounded Answer: $34$

10) Calculator Answer: $716$, Rounded Answer: $720$

11) Calculator Answer: $\approx90.90909\cdots$, Rounded Answer: $91$

12) Calculator Answer: $\approx1323.2$, Rounded Answer: $1320$

13) Calculator Answer: $1.5738\times 10^{3}$, Rounded Answer: $1.57\times 10^{3}$

14. Rounding to three significant figures

a) $0.0155m$ or $1.55\times 10^{-2}m$

b) $9010m$ or $9.01\times 10^{3}m$

c) $1.78\times 10^{3}m$

d) $630m$ or $6.30\times 10^{2}m$

e) $9460m$ or $9.46\times 10^{3}m$

f) $40000g$ or $4.00\times 10^{4}g$

15. Volume of the warehouse

$1300m^{3}$ or $1.3\times 10^{3}m^{3}$