Standard Form Questions Solutions - Week 3 PDF

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Standard Form Questions Solutions - Week 3...

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Standard Form Exercises

1. Multiplication a. (4 x 103) x (2 x 105)

= 8 x 108

b. (5 x 106) x (4 x 109)

= 20 x 1015

c. (2.5 x 10-3) x (5 x 10-8)

= 2.0 x 1016

= 12.5 x 10-11 = 1.25 x 10-10

2. Division a. (8 x 105) ÷ (2 x 103)

= 4 x 102

b. (9 x 102) ÷ (3 x 10-4)

= 3 x 106

3. Addition

a. (2 x 102) + (3 x 103) = (0.2 x 103) + (3 x 103) = 3.2 x 103 b. (7.1 x 103) + (2.4 x 102)

= (7.1 x 103) + (0.24 x 103) = 7.34 x 103

c. (5.2 x 104) + (3.2 x 102)

= (5.2 x 104) + (0.032 x 104) = 5.234 x 104

4. Subtraction

a. (1 x 10-1) – (2 x 10-2)

= (10 x 10-2) – (2 x 10-2) = 8 x 10-2

b. (3.4 x 103) – (2 x 101) = (3.4 x 103) – (0.02 x 103) = 3.38 x 103 5. Work out (13.8 × 107) × (5.4 × 10–12) Give your answer as an ordinary number.

(13.8 × 107) × (5.4 × 10–12) = 74.52 x 10-5 = 0.0007452 7.97 × 10−6

6. Write

as an ordinary number.

0.00000797 7. Work out the value of (2.52 × 105) ÷ (4 × 10−3) Give your answer in standard form. (2.52 × 105) ÷ (4 × 10−3) = 0.63 × 108 = 6.3 × 107 8. Write

0.000451 4.51 ×

9. Work out

in standard form.

10-4

7.8 × 105 2.4 × 10−4

Give your answer in standard form.

(7.8 × 105) ÷ (2.4 × 10−4) = 3.25 × 109 10. Write these numbers in order of size. Start with the smallest number. 0.0034 × 105

34 × 10−5

-3.4 × 10−3

34 × 10−5

−3.4 × 10−3 0.0034 × 105

3.4 × 104 34 × 102

34 × 102 3.4 × 104

Standard Form Exercises

11. 2.2 × 107 passengers passed through Beijing Capital International Airport in 2014. (a) Write 2.2 × 107 as an ordinary number.

22 000 000

950 000 tonnes of cargo traffic passed through Tokyo International Airport in 2014. 9.5 x 105

(b) Write 950 000 as a number in standard form.

12. The mass of the Sun is 2 × 1030 kg. The mass of the largest known star is 315 times the mass of the Sun. Work out the mass of this star. Give your answer in kg in standard form. (2 × 1030) x 315 = 630 × 1030 = 6.30 × 1032 kg 13. An object is travelling at a speed of 2650 metres per second. How many seconds will the object take to travel a distance of 3.45 × 1010 metres? Give your answer in standard form, correct to 2 significant figures. Speed = distance / time

time = distance / speed

Time = 3.45 x 1010 / 2650 = 0.0013018867 x 1010 = 1.3 x 107 Challenge Questions 𝑥−𝑦 14. p2 = 𝑥𝑦

x = 8.5 × 109

and

y = 4 × 108

Find the value of p. Give your answer in standard form correct to 2 significant figures. (8.5 × 109 ) − (0.4 × 109 ) (8.5 × 109 )−(4 × 108 ) = (8.5 × 109 )×(4 × 108 ) (8.5 × 109 )×(4 × 108 ) (8.1 × 109 ) p2 = = 0.2382352 x 10-8 (34 × 1017)

p2 =

p = √0.238 x 10−8

= 0.4880934 x 10-4

p = 4.9 x 10-5 15. m = 8 × 109n where n is an integer. Express in standard form. Give your answer, in terms of n, as simply as possible. (8 × 109𝑛 ) =

1 −3

1 (2 × 103𝑛 )

= 5 × 10−3𝑛−1

=

1 (8 × 109𝑛)

= 0.5 × 10−3𝑛

1 3

or

(2 × 103𝑛 )

−1

Standard Form Exercises

16. A spacecraft travels from Earth to Mars at an average speed of 13 km/s to the nearest km/s. The spacecraft travels a distance of 1.4 x 108 miles to 2 significant figures. Calculate the number of days the spacecraft takes to travel from Earth to Mars. You may use 1 mile = 1.6 km 1 km/s = 2250 miles per hour. Speed = 13 km/s = 13 x 2250 = 29250 = 2.9250 x 104 miles per hour Time = 1.4 x 108 / 2.9250 x 104 = 0.478623 x 104 hours Time = (0.478623 x 104) / 24 = 0.019943 x 104 = 199 days

17. One sheet of paper is 9 x 10-3 cm thick to 1 significant figure. Mark wants to put 500 sheets of paper into the paper tray of his printer. The paper tray is 5.0 cm deep to 1 decimal place. Can Mark be sure that the paper tray is deep enough for 500 sheets of paper? Taking a simple approach Thickness of paper = 500 x 9 x 10-3 = 4.5 cm The tray is 5.00 cm deep Yes it is deep enough However, to be sure that the paper will fit, allow for the errors introduced by rounding to 1 significant figure and 1 decimal place The maximum thickness of paper (allowing for rounding down to 1 sf. +/- 0.5 x 10-3) = 500 x 9.5 x 10-3 = 4.75 cm The minimum depth of the tray = 4.5 cm No possibly not....