The distance between the Earth and Mars is at least 56 000 000 km. Write this distance in the form $a \times 10^n$ km, where $1 \leq a < 10$ and $n \in \mathbb{N}$. The diameter of a human hair is roughly 0.0075 cm. Write this diameter in the form $b \times 10^n$ cm, where $1 \leq b < 10$ and $n \in \mathbb{Z}$. Lewis was driving at 90 km per hour when he sneezed. During the sneeze, his eyes were closed for half a second. Work out how many metres he travelled in this time.

Junior Cycle Mathematics Applied Measure - Area, Volume, Speed, Distance: The distance between the Earth a

The distance between the Earth and Mars is at least 56 000 000 km - Junior Cycle Mathematics - Question 3 - 2019

Question 3

The distance between the Earth and Mars is at least 56 000 000 km. Write this distance in the form $a \times 10^n$ km, where $1 \leq a < 10$ and $n \in \mathbb{N}$. ... show full transcript

Worked Solution & Example Answer:The distance between the Earth and Mars is at least 56 000 000 km - Junior Cycle Mathematics - Question 3 - 2019

Step 1

Write this distance in the form $a \times 10^n$ km

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Answer

To express 56,000,000 in the form $a \times 10^n$ , we first rewrite it in scientific notation:

Move the decimal point 7 places to the left, which yields: $5.6 \times 10^7 \text{ km}$

Thus, the answer is $5.6 \times 10^7$ km.

Step 2

Write this diameter in the form $b \times 10^n$ cm

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Answer

The diameter of a human hair is given as 0.0075 cm. To express this in scientific notation:

Move the decimal point 3 places to the right: $7.5 \times 10^{-3} \text{ cm}$

Thus, the answer is $7.5 \times 10^{-3}$ cm.

Step 3

Work out how many metres he travelled in this time

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Answer

To find how far Lewis travelled during the sneeze:

Convert his speed from km/h to m/s:
- First, convert km/h to m/min:
  
  $90 \text{ km/h} = 90 \times 1000 \text{ m/h} = 90000 \text{ m/h}$
- Then convert hours to minutes:
  
  $90000 \text{ m/h} \div 60 = 1500 \text{ m/min}$
- Now convert minutes to seconds:
  
  $1500 \text{ m/min} \div 60 = 25 \text{ m/s}$
Calculate the distance travelled during half a second:

$ext{Distance} = ext{Speed} \times ext{Time} = 25 \text{ m/s} \times 0.5 \text{ s} = 12.5 \text{ m}$

Thus, Lewis travelled 12.5 metres during the sneeze.

The distance between the Earth and Mars is at least 56 000 000 km - Junior Cycle Mathematics - Question 3 - 2019

Worked Solution & Example Answer:The distance between the Earth and Mars is at least 56 000 000 km - Junior Cycle Mathematics - Question 3 - 2019

Write this distance in the form $a \times 10^n$ km

Write this diameter in the form $b \times 10^n$ cm

Work out how many metres he travelled in this time

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