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Worksheets

Significant Figures, Scientific Notation & Operations

Total questions: 45

Worksheet time: 55mins

Name
Class
Date
1.

Luna measured the length of a bookshelf and found it to be 78.5 cm. What is 78.5 rounded to one significant figure?

a)

79

b)

78.5

c)

70

d)

80

2.

Grace is measuring the thickness of a thin film and her instrument shows a value of 0.010229 mm. She needs to report the measurement rounded to four significant figures. What value should she record?

a)

1022

b)

1023

c)

0.01023

d)

0.01022

3.

Avery measures the length of a pencil and finds it to be 0.658 meters. What is the length rounded to 1 significant figure?

a)

0

b)

0.66

c)

0.7

d)

0.658

4.

Aiden is helping his teacher in the science lab and measures the length of a pencil to be 7.555 cm. What is the length rounded to two significant figures?

a)

7.6

b)

7.5

c)

70

d)

76

e)

7.60

5.

Jackson is analyzing the population of a small town, which is currently 52689. He needs to round this number to 3 significant figures for his report. What should Jackson write in his report?

a)

526

b)

527

c)

52600

d)

52700

6.

Samuel is working in a laboratory and needs to record the thickness of a thin wire for an experiment. He measures the wire and gets a value of 0.00258954 meters. Round this measurement to 4 significant figures.

a)

0.0025

b)

0.002589

c)

0.002580

d)

0.002590

7.

Emma counted 1235 people at a concert. Round this number to 2 significant figures.

a)

12

b)

1200

c)

1200.

d)

1200.00

8.

James is calculating the momentum of a box by multiplying its mass and velocity:

6.08 kg×5.0 ms6.08\ kg\times5.0\ \frac{m}{s}  

How many significant figures are in the result for this calculation?

a)

3 significant figures

b)

1 significant figure

c)

2 significant figures

d)

4 significant figures

e)

5 significant figures

9.

Arjun is measuring the power output of a device. He records an energy transfer of 65.3 J over a time interval of 50.085 s. How many significant figures are in the result for the following calculation?

65.3 J50.085 s\frac{65.3\ J}{50.085\ s}  

a)

5 significant figures

b)

2 significant figures

c)

1 significant figure

d)

3 significant figures

10.

James is measuring the length of two pieces of rope for a project. The first rope is 25.085 m25.085\ m long, and the second rope is 16.2 m16.2\ m long. What is the total length of rope James has? Ensure that the correct number of significant figures are included in the calculated result.

a)

41.3 m

b)

41.2085 m

c)

41.285 m

d)

41.2 m

11.

Noah is timing a race. He starts his stopwatch and records a time of 12.582 s12.582\ s when the runner finishes. However, he realizes he started the stopwatch 5.23 s5.23\ s after the race began. What is the actual time it took for the runner to finish the race? Ensure that the correct number of significant figures are included in the calculated result.

a)

7.360 s

b)

7.36 s

c)

7.35 s

d)

7.352 s

e)

7.350 s

12.

Ethan is preparing a chemical mixture and needs to add the following masses of different substances:

17.2 g + 9 g + 36.333 g + 0.58 g17.2\ g\ +\ 9\ g\ +\ 36.333\ g\ +\ 0.58\ g  

For significant figures, which term is the limiting term in this calculation?

a)

17.2 g

b)

9 g

c)

36.33 g

d)

0.58 g

13.

Olivia is measuring the length of a table, and the true length is 25.0 cm. Which set of measurements demonstrates accuracy and precision?

a)

19.9 cm

20.0 cm

20.0 cm

20.1 cm

20.2 cm

b)

24.8 cm

24.9 cm

25.0 cm

25.0 cm

25.1 cm

c)

17.2 cm

18.9 cm

19.8 cm

20.0 cm

22.0 cm

d)

23.5 cm

24.9 cm

25.0 cm

26.3 cm

26.5 cm

14.

Emma is buying 3.02 meters of ribbon, and each meter costs 2.3 dollars. Use the correct significant figure to calculate the final answer for the total cost.

3.02×2.3=3.02\times2.3=  

a)

6.946

b)

6.95

c)

6.9

d)

7.0

15.

Olivia is calculating the total number of bacteria in two samples. The first sample has 1 x 1061\ x\ 10^6 bacteria, and the second sample has 7 x 1087\ x\ 10^8 bacteria. What is the total number of bacteria in both samples?

a)

8 x 10488\ x\ 10^{48}  

b)

7 x 10487\ x\ 10^{48}  

c)

7 x 10147\ x\ 10^{14}  

d)

None of the Choices

16.

Hannah is measuring the lengths of four different rods for a science experiment. She records the following lengths: 3.419 m, 3.912 m, 7.0518 m, and 0.00013 m. Give the total length to the correct number of significant figures.

a)

14.383

b)

14.382

c)

14.3829

d)

14.38293

17.

Anika is measuring the length of a piece of ribbon. She finds that the original length is 145.63 cm, but she needs to cut off 28.9 cm.
What is the length of the ribbon left, giving your answer to the correct number of significant figures?

a)

116.73

b)

116.7

c)

116.70

d)

117

18.

Abigail is measuring the efficiency of a machine. She records that the machine outputs 247.89 joules of energy and requires 43.5 joules of input energy. Give the efficiency to the correct number of significant figures for

247.89 ÷ 43.5

a)

5.70

b)

5.7

c)

5.699

d)

5.69

19.

Scarlett has a ribbon that is 129.6 cm long. She wants to cut it into 3 equal pieces. What is the length of each piece? Give your answer with the correct number of significant figures.
129.6/3

a)

43.0

b)

43

c)

 4x101

d)

40.0

20.

Mia is calculating the total area of a rectangular field. The length of the field is 12.470 meters and the width is 271 meters. Solve and give your answer with the correct number of significant figures
(12.470)(271)

a)

3366.9

b)

3.370x103

c)

3400

d)

3370

21.

Samuel is measuring the area of a rectangular table. The length of the table is 1.23 m and the width is 0.89 m. Calculate the area and give your answer with the appropriate number of significant figures.

a)

1.0 m2

b)

1.1 m2

c)

1.0947 m2

d)

1.09 m2

22.

Lucas finds a rock during a hike and measures its mass as 0.0472 kg. What is the mass rounded to two significant figures?

a)

0.048

b)

0.05

c)

0.0470

d)

0.047

23.

Sophia is calculating the volume of a box. The length is 2.56 m, the width is 1.4 m, and the height is 0.85 m. What is the volume, using the correct number of significant figures?

a)

3.05 m3

b)

3.0472 m3

c)

3.04 m3

d)

3.0 m3

24.

Ella is conducting a science experiment and records the temperature as 36.789°C. Round this value to three significant figures.

a)

36.7°C

b)

36.8°C

c)

36.789°C

d)

36.8

25.

Isabella is working in a laboratory and measures the mass of a chemical sample as 0.003456 kg. What is the mass rounded to three significant figures?

a)

0.0035 kg

b)

0.00345 kg

c)

0.0034 kg

d)

0.00346 kg

26.

Benjamin is working in a laboratory and measures the length of a metal rod as 18.72 cm. He needs to report the length rounded to two significant figures for his lab report. What value should he write?

a)

18.7 cm

b)

18 cm

c)

18.72 cm

d)

19 cm

27.

Chloe is calculating the total mass of two objects. The first object has a mass of 2.34 g and the second has a mass of 0.9 g. What is the total mass, using the correct number of significant figures?

a)

3.0 g

b)

3.3 g

c)

3.24 g

d)

3.2 g

28.

Mia measures the mass of a bag of flour as 2.345 kg. What is the mass rounded to two significant figures?

a)

2.3 kg

b)

2.35 kg

c)

2.4 kg

d)

2.34 kg

29.

Henry is timing how long it takes for a chemical reaction to complete in his laboratory. He records the time taken as 0.008763 s. Round this value to three significant figures.

a)

0.00877 s

b)

0.00876 s

c)

0.0088 s

d)

0.00876

30.

Ava is calculating the area of a rectangle. The length is 4.56 m and the width is 2.1 m. What is the area, using the correct number of significant figures?

a)

9.6 m2

b)

9.58 m2

c)

9.576 m2

d)

9.5 m2

31.

Lily is measuring the mass of a tiny grain of sand and finds it to be 0.00056 grams. How should she express this mass in scientific notation?

a)

5.6 x 10-4

b)

5.6 x 10-5

c)

5.6 x 10-3

d)

56 x 10-5

32.

Sophia is writing the distance from Earth to a nearby star in scientific notation. Which of the following numbers is correctly written in scientific notation?

a)

230 x 103

b)

2.3 x 105

c)

23 x 104

d)

0.23 x 105

33.

Charlotte is reading a science book and comes across the number 4.2 x 103. She wants to write it in standard decimal notation. What number should Charlotte write?

a)

42,000

b)

0.0042

c)

4200

d)

420

34.

Aria is reading about the population of a large city, which is 3,500,000 people. How should Aria express this number in scientific notation?

a)

3.5 x 106

b)

3.5 x 107

c)

3.5 x 105

d)

35 x 105

35.

Maya is writing the mass of a grain of rice in scientific notation for her science project. Which of the following numbers is correctly written in scientific notation?

a)

450 x 100

b)

0.45 x 103

c)

4.5 x 102

d)

45 x 101

36.

Jackson is measuring the concentration of a chemical in a solution. His result is 7.2 x 10-4 mol/L. What is this value in standard decimal notation?

a)

0.00072

b)

0.0072

c)

0.00072

d)

0.00072

37.

Grace is calculating the total number of bacteria in two samples. The first sample contains 2.5×1032.5\times10^3 bacteria, and the second sample contains 4.0×1024.0\times10^2 times as many bacteria as the first. Which of the following is the correct result for the total number of bacteria in both samples, expressed in scientific notation?

a)

1.0 x 106

b)

10 x 105

c)

1.0 x 107

d)

1.0 x 105

38.

Aria is conducting an experiment and measures two very small quantities: (2 x 10-5) grams of a substance in one sample and (7 x 10-5) grams in another. What is the total mass of the substance Aria has measured?

a)

9 x 10-10

b)

14 x 10-5

c)

9 x 10-5

d)

1.4 x 10-4

39.

Mia is collecting stamps. She has collected (5 x 106) stamps so far, but she decides to give away (3 x 106) stamps to her friend. How many stamps does Mia have left?

a)

2 x 1012

b)

2 x 106

c)

2 x 1036

d)

2 x 100

40.

Daniel is calculating the total number of bacteria in a lab experiment. He starts with 2 x 109 bacteria, and each bacterium multiplies by 4 x 10-4 times during the experiment. What is the total number of bacteria at the end?

a)

8 x 1013

b)

8 x 1036

c)

8 x 105

d)

8 x 10-36

41.

Kai is calculating the total number of bacteria in two petri dishes. The first dish has 5 x 106 bacteria, and the second dish has 5 x 107 bacteria. If he multiplies the number of bacteria in both dishes, what is the result?

a)

2.5 x 1012

b)

2.5 x 1014

c)

25 x 1012

d)

25 x 1013

42.

Emma is working in a laboratory and has a container with 5 x 1012 bacteria. She wants to distribute them equally into 2 x 106 petri dishes.
How many bacteria will each petri dish contain?
------------

a)

2.5 x 102

b)

2.5 x 106

c)

3 x 102

d)

2.5 x 1018

43.

Benjamin has 6 x 106 liters of water stored in a reservoir. He wants to distribute this water equally into containers, each with a capacity of 2 x 103 liters. How many containers can Benjamin fill?

a)

12 x 103

b)

3 x 109

c)

1.2 x 104

d)

3 x 103

44.

Mia is organizing a charity event. She expects 3.8 x 104 people to attend, but due to a scheduling conflict, 2 x 103 people cancel their plans. What is the difference in the expected number of attendees?
(3.8 x 104) - (2 x 103)

a)

1.8 x 104

b)

1.8 x 101

c)

3.6 x 101

d)

3.6 x 104

45.

Oliver is planning a morning jog. He starts at his house and jogs a distance of 8.2 km. After covering 3 x 102 m, he checks how much farther he has to go. How much distance does Oliver have left to jog?

a)

5.2 x 10-2 m

b)

8.107 x 102 m

c)

7.9 x 101 km

d)

11.2 x 10-2 m