Question

homework - significant figure practice
use scrap paper to help calculate the following using the proper number of significant figures. place your final answer in scientific notation.

1. 12.25 m + 3.07 m =
2. 76.032 cm + 0.123 cm =
3. 45.236 dal + 9.4 dal =
4. 0.0102 g + 146.2 g =
5. 7294.69 mm + 0.00235 mm =
6. 0.0036 l + 0.1234 l =
7. 0.00470 kg + 0.000923 kg =
8. 3.024 m - 0.0017 m
9. 10.9 g - 0.14 g =
10. 1.00238 kg - 0.0146 kg =
11. 0.000463 km - 0.0000279 km =
12. 968.0049 hl - 1.996 hl =
13. 9.362 dm - 0.01 dm =
14. 0.0354 m - 0.0269 m =
15. 3.2 cm x 6.7 cm =
16. 4.734 l x 120 l =
17. 201 g x 123 g =
18. 0.004 mm x 3 mm =
19. 400 kg x 0.066 kg =
20. 0.00400 s x 0.066 s =
21. 4.0 mg x 0.01003 mg =
22. 7.2 kg ÷ 0.9 kg =
23. 100 m ÷ 22 m =
24. 14.4 gg ÷ 40.0 gg =
25. 1200 s ÷ 3.0 s =
26. 5600 cm ÷ 140 cm =
27. 76.024 l ÷ 0.00370 l =
28. 87.9 m ÷ 7346.2 m =

Explanation:

Step1: Perform addition/subtraction

For addition and subtraction, the result should be rounded to the same number of decimal - places as the number with the fewest decimal places in the values being added or subtracted.

Step2: Perform multiplication/division

For multiplication and division, the result should have the same number of significant figures as the number with the fewest significant figures in the values being multiplied or divided.

Step3: Convert to scientific notation

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

1. $12.25\ m+3.07\ m = 15.32\ m=1.532\times 10^{1}\ m$
2. $76.032\ cm + 0.123\ cm=76.155\ cm = 7.6155\times 10^{1}\ cm$
3. $45.236\ daL+9.4\ daL = 54.636\ daL\approx54.6\ daL = 5.46\times 10^{1}\ daL$
4. $0.0102\ g+146.2\ g = 146.2102\ g\approx146.2\ g=1.462\times 10^{2}\ g$
5. $7294.69\ mm+0.00235\ mm = 7294.69235\ mm\approx7294.69\ mm = 7.29469\times 10^{3}\ mm$
6. $0.0036\ L+0.1234\ L = 0.127\ L=1.27\times 10^{-1}\ L$
7. $0.00470\ kg+0.000923\ kg = 0.005623\ kg\approx0.00562\ kg = 5.62\times 10^{-3}\ kg$
8. $3.024\ m - 0.0017\ m=3.0223\ m\approx3.022\ m = 3.022\times 10^{0}\ m$
9. $10.9\ g-0.14\ g = 10.76\ g\approx10.8\ g = 1.08\times 10^{1}\ g$
10. $1.00238\ kg-0.0146\ kg = 0.98778\ kg\approx0.988\ kg = 9.88\times 10^{-1}\ kg$
11. $0.000463\ km-0.0000279\ km = 0.0004351\ km\approx0.000435\ km = 4.35\times 10^{-4}\ km$
12. $968.0049\ hL-1.996\ hL = 966.0089\ hL\approx966.01\ hL = 9.6601\times 10^{2}\ hL$
13. $9.362\ dm-0.01\ dm = 9.352\ dm\approx9.35\ dm = 9.35\times 10^{0}\ dm$
14. $0.0354\ m-0.0269\ m = 0.0085\ m = 8.5\times 10^{-3}\ m$
15. $3.2\ cm\times6.7\ cm = 21.44\ cm^{2}\approx21\ cm^{2}=2.1\times 10^{1}\ cm^{2}$
16. $4.734\ L\times120\ L = 568.08\ L^{2}\approx570\ L^{2}=5.7\times 10^{2}\ L^{2}$
17. $201\ g\times123\ g = 24723\ g^{2}\approx24700\ g^{2}=2.47\times 10^{4}\ g^{2}$
18. $0.004\ Mm\times3\ Mm = 0.012\ Mm^{2}=1.2\times 10^{-2}\ Mm^{2}$
19. $400\ kg\times0.066\ kg = 26.4\ kg^{2}\approx26\ kg^{2}=2.6\times 10^{1}\ kg^{2}$
20. $0.00400\ s\times0.066\ s = 0.000264\ s^{2}\approx2.6\times 10^{-4}\ s^{2}$
21. $4.0\ mg\times0.01003\ mg = 0.04012\ mg^{2}\approx0.040\ mg^{2}=4.0\times 10^{-2}\ mg^{2}$
22. $7.2\ kg\div0.9\ kg = 8 = 8\times 10^{0}$
23. $100\ m\div22\ m\approx4.5 = 4.5\times 10^{0}$
24. $14.4\ Gg\div40.0\ Gg = 0.36 = 3.6\times 10^{-1}$
25. $1200\ s\div3.0\ s = 400 = 4.0\times 10^{2}$
26. $56.00\ cm\div140\ cm\approx0.40 = 4.0\times 10^{-1}$
27. $76.024\ L\div0.00370\ L\approx20547.027\approx2.05\times 10^{4}$
28. $87.9\ m\div7346.2\ m\approx0.011965\approx1.20\times 10^{-2}$

Answer:

1. $1.532\times 10^{1}\ m$
2. $7.6155\times 10^{1}\ cm$
3. $5.46\times 10^{1}\ daL$
4. $1.462\times 10^{2}\ g$
5. $7.29469\times 10^{3}\ mm$
6. $1.27\times 10^{-1}\ L$
7. $5.62\times 10^{-3}\ kg$
8. $3.022\times 10^{0}\ m$
9. $1.08\times 10^{1}\ g$
10. $9.88\times 10^{-1}\ kg$
11. $4.35\times 10^{-4}\ km$
12. $9.6601\times 10^{2}\ hL$
13. $9.35\times 10^{0}\ dm$
14. $8.5\times 10^{-3}\ m$
15. $2.1\times 10^{1}\ cm^{2}$
16. $5.7\times 10^{2}\ L^{2}$
17. $2.47\times 10^{4}\ g^{2}$
18. $1.2\times 10^{-2}\ Mm^{2}$
19. $2.6\times 10^{1}\ kg^{2}$
20. $2.6\times 10^{-4}\ s^{2}$
21. $4.0\times 10^{-2}\ mg^{2}$
22. $8\times 10^{0}$
23. $4.5\times 10^{0}$
24. $3.6\times 10^{-1}$
25. $4.0\times 10^{2}$
26. $4.0\times 10^{-1}$
27. $2.05\times 10^{4}$
28. $1.20\times 10^{-2}$