Standard Form Questions

Standard Form Questions

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Part A

Express the following numbers in Standard Form.

1. 300

2. 5,100

3. 72,040.4

4. 119,988.7

5. 6,320,110

6. 1,000,100,000

7. 8,108,136

8. 77,012

9. 1.72

10. 34.7

11. 0.001

12. 0.00034

13. 0.9

14. 0.801

15. 0.01087

16. 0.00009

17. 0.031

18. 0.000000701

19. 0.00008632

20. 0.11

Part B

Express the following numbers as an ordinary value.

1. 3 x 102

2. 4.71 x 103

3. 2.401 x 105

4. 7.42 x 106

5. 1.1111 x 103

6. 1.5 x 10-1

7. 3.01 x 10-4

8. 9.89 x 10-6

9. 3.456 x 10-7

10. 1.234 x 10-1

Part C

1. Light travels approximately 300,000,000 metres each second. A light year is the total distance travelled by light in one year. Assuming there are 365 days in a year, determine a light year, expressing your answer in Standard Form (and with the correct unit!).

2. The radius of the Earth is 4.0075 x 104 km.

a. What is the circumference of the Earth in metres, in Standard Form?

b. How many times can light fully encircle the Earth per second?

3. A ‘bit’ is the smallest unit of space in computing (holding a ‘0’ or ‘1’ value). There are 8 bits in a byte, 210 bytes in a kilobyte, 210 kilobytes in a megabyte, 210 megabytes in a gigabyte and 210 gigabytes in a terabyte. The size of the internet is approximately 5 x 106 terabytes. How many bits are there on the internet (in Standard Form)?

Part D

Bob the Rubbish Mathematician has failed to put these numbers in Standard Form correctly. Fix them up.

1. 30×103

2. 400×109

3. 0.1 ×107

4. 33×10-9

5. 4210×101

6. 0.092×10-3

7. 0.0002×103

Part E

Determine the result of these following multiplications and divisions.

1. 3×104×3×104

2. 1×102×4.2×103

3. 2×10-2×4×104

4. 3.1×105×4×106

5. 6×101×7×102

6. 9×10-3×8.1×107

7. 1.2×1010×9×10-2

8. 9×1073×104

9. 2×1091×102

10. 1×1054×103

11. 1×1055×107

12. 2×1038×10-4

13. 7.1×1052.2×109

14. 1.1×10-34.8×10-4

If you have reached this point, then you have won. Well done. Have a milkshake or something.

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Standard Form Questions - ANSWERS

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Part A

Express the following numbers in Standard Form.

1. 300 =3×102

2. 5,100 =5.1×103

3. 72,040.4=7.20404×104

4. 119,988.7=1.199887×105

5. 6,320,110=6.32011×106

6. 1,000,100,000
=1.0001×109

7. 8,108,136
=8.108136×106

8. 77,012 =7.7023×104

9. 1.72=1.72×101

10. 34.7=3.47×102

11. 0.001 =1×10-3

12. 0.00034 =3.4×10-4

13. 0.9 =9×10-1

14. 0.801 =8.01×10-1

15. 0.01087 =1.087×10-2

16. 0.00009 =9×10-5

17. 0.031 =3.1×10-2

18. 0.000000701 =7.01×10-7

19. 0.00008632 =8.632×10-5

20. 0.11 =1.1×10-1

Part B

Express the following numbers as an ordinary value.

1. 3 x 102 =300

2. 4.71 x 103 =4710

3. 2.401 x 105 =240100

4. 7.42 x 106 =7420000

5. 1.1111 x 103 =1111.1

6. 1.5 x 10-1 =0.15

7. 3.01 x 10-4 =0.000301

8. 9.89 x 10-6 =0.00000989

9. 3.456 x 10-7
=0.0000003456

10. 1.234 x 10-1 =0.1234

Part C

=9.4608×1015

2. The radius of the Earth is 6378.1km.

a. What is the circumference of the Earth in metres, in Standard Form?
=4.0075×107m

b. How many times can light fully encircle the Earth per second?
= 7.48 times

Part D

Bob the Rubbish Mathematician has failed to put these numbers in Standard Form correctly. Fix them up.

1. 30×103 =3×104

2. 400×109=4×1011

3. 0.1 ×107=1×106

4. 33×10-9=3.3×10-8

5. 4210×101=4.21×104

6. 0.092×10-3=9.2×10-5

7. 0.0002×103=2×10-1

Part E

Determine the result of these following multiplications and divisions.

1. 3×104×3×104=9×108

2. 1×102×4.2×103=4.2×105

3. 2×10-2×4×104=8×102

4. 3.1×105×4×106=1.24×1012

5. 6×101×7×102=4.2×104

6. 9×10-3×8.1×107=7.20×105

7. 1.2×1010×9×10-2=1.08×109

8. 9×1073×104=3×103

9. 2×1091×102=2×107

10. 1×1054×103=2.5×101

11. 1×1055×107=2×10-3

12. 2×1038×10-4=2.5×106

13. 7.1×1052.2×109=3.23×10-4

14. 1.1×10-34.8×10-4=2.29×100 or 2.29