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