SCIENTIFIC NOTATIONAND SIGNIFICANT FIGURES

Junior Cert Revision

Write 868 million in the form 𝑎 × 10𝑛, where 𝑛 ∈ ℤ and 1 ≤ 𝑎 < 10, 𝑎 ∈ ℝ.

2017 JCHL Paper 1 – Question 3 (a)

868 million = 868,000,000

= 8.68 × 108

During the Apollo-11 mission, it took approximately 1∙3 seconds for a radio signal to travel 380 000 km.Find the average speed of the radio signal, in km per minute. Give your answer in the form 𝑎 × 10𝑛, where 𝑛 ∈ ℤ and where 1 ≤ 𝑎 < 10 is correct to two decimal places.

2017 JCHL Paper 1 – Question 3 (b)

=380,000

1.3

= 292307.6923 km/s

= 17538461.54 km/m

= 1.75 × 107

Speed =Distance

Time

Answer to two decimal places. Always read the question one more time.

This is km per second. Multiply by 60 to get km per minute.

In 2016, a spacecraft flew around Jupiter, 868 million km from earth.Find how many minutes it would take a radio signal to travel 868 million km.Assume that the radio signal would travel at the same speed as your answer to part (b).

2017 JCHL Paper 1 – Question 3 (c)

=8.68 × 108

1.75 × 107

= 49.6 minutes

Speed =Distance

Time

How many digits does the number 3.14 × 10100 have, when it is written out fully?Justify your answer.

2016 JCHL Paper 1 – Question 6 (c)

3.14 × 10100

100 + 1 = 101 digits

The power 100, indicates that are 100 places after the first 3, so there are 101 digits including the first 3.

Express 224 in the form 𝑎 × 10𝑛, where 1 ≤ 𝑎 ≤ 10 and 𝑛 ∈ 𝑍, correct to three significant figures.

2014 LCOL Sample Paper 1 – Question 1 (b)

224 = 16,777,216

= 1.68 × 107

First put the number in the calculator.

Significant figures are digits that carry meaning. All numbers EXCEPT for leading 0’s. In this case 1, 6 and 8 are significant. We round the 3rd

number up because the next number after it is ≥ 5.

The mean distance from the earth to the sun is 149 597 871 km. Write this number in the form 𝑎 × 10𝑛, where 1 ≤ 𝑎 ≤ 10 and 𝑛 ∈ 𝑍, correct to two significant figures.

2013 LCOL Paper 1 – Question 3 (a)

149 597 871= 1.5 × 108

Significant figures are digits that carry meaning. All numbers EXCEPT for leading 0’s. In this case 1 and 5 are significant. We round the 2nd number up because the next number is ≥ 5.

The number 261 − 1 is a prime number. Using your calculator, or otherwise, express its value, correct to two significant figures, in the form 𝑎 × 10𝑛, where 1 ≤ 𝑎 < 10 and 𝑛 ∈ ℕ.

2011 LCOL Paper 1 – Question 1 (c)

Use your answer to part (c) to state how many digits there are in the exact value of 261 − 1.

2011 LCOL Paper 1 – Question 1 (d)

261 − 1= 2.3 × 1018

Put the number in the calculator.

The power 18, indicates that are 18 places after the 2, so there are 19 digits including the 2.

19 Digits

€3.6 billion = 3,600,000,000€700 million = 700,000,000

3,600,000,000 +700,000,000

4,300,000,000

= 4.3 × 109

Given that 1 billion is a thousand million, find the sum of €3.6 billion and €700 million.Give your answer in the form 𝑎 × 10𝑛 where 𝑛 ∈ ℕ and 1 ≤ 𝑎 < 10.

2012 JCHL Paper 1 – Question 3 (a)

There are 7 digits in 1 million and 10 digits in 1 billion.

The diameters of Venus and Saturn are 1.21 × 104 kmand 1.21 × 105 km.What is the difference between the diameters of the two planets. Give your answer in the form 𝑎 × 10𝑛 where 𝑛 ∈ ℤ and 1 ≤ 𝑎 < 10.

2011 JCHL Paper 1 – Question 1 (b) (i)

1.21 × 105 = 121,000 km1.21 × 104 = 12,100 km

121,000 −12,100

108,900

1.089 × 105 km

The population of china is 1.351 × 109.Write this as a whole number of people.

2011 LCFL Paper 1 – Question 1 (b)

1.351 × 109

= 1,351,000,000

One billion, 351 million.

The mass of Jupiter is 1.9 × 1027 kg and the mass of earth is 5.97 × 1024 kg. How many times greater is the mass of Jupiter than the mass of earth?

2014S LCFL Paper 1 – Question 1 (b) (i)

1.9 × 1027

5.97 × 1024

= 318.258

≈ 318 times greater