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TEST CORRECTIONS Test #03

› Standard Index Form

If you failed Question 1 in the test, you must do these 3 extra questions:

a) Convert each of these three numbers from Standard Index Form to ordinary numbers (Full Numerical Form):

i) \(2.236\times 10^3\)

ii) \(4.3\times 10^4\)

iii) \(3.1\times 10^{-4}\)

Hints

Part (i):

  2 × 10³ can be written as:
	
        ┌──────────┤Chucking in loads of meaningless zeros after the decimal-point
    ╒═╤═╪═╤═╕
  2.0 0 0 0 0 × 10³          
         
                  ╔═════════════╗
                  ▼             ╟————————————————————————————————————————————————————————————————╖
  2.0 0 0 0 0 × 10³            	║ Every time we move the decimal right, we knock 1 off the power ║
                                ║      So, we have to move the decimal right by ‘3’ places       ║
                                ║                to get this power down to zero                  ║
So, the number becomes:         ╙————————————————————————————————————————————————————————————————╜
         
         
  2.0 0 0.0 0 × 10⁰           =   2000.00  =  2000
  │ ▲ ▲ ▲
  └─┘─┘─┘ 
moving the decimal
right by 3 places

Hints

Part (ii):

  4.3 × 10⁴ can be written as:
	
          ┌──────────┤ Bung in loads of meaningless zeros after the decimal-point
      ╒═╤═╪═╤═╕
  4.3 0 0 0 0 0 × 10⁴ 
         
                    ╔═══════════╗
                    ▼           ╟————————————————————————————————————————————————————————————————╖
  4.3 0 0 0 0 0 × 10⁴          	║ Every time we move the decimal right, we knock 1 off the power ║
                                ║      So, we have to move the decimal right by ‘4’ places       ║
                                ║                to get this power down to zero                  ║
So, the number becomes:         ╙————————————————————————————————————————————————————————————————╜
         
         
  4.3 0 0 0.0 0 × 10⁰   =   43000.00  =  ......
  │ ▲ ▲ ▲ ▲
  └─┘─┘─┘─┘
moving the decimal
right by 4 places

Hints

Part (iii):

            3.1 × 10^-4 can be written as:
	
      ┌──────────┤Putting in loads of meaningless zeros before any digits
  ╒═╤═╪═╤═╕
  0 0 0 0 0 3.1 × 10^-4 
         
                    ╔═══════════╗
                    ▼           ╟——————————————————————————————————————————————————————————————╖
  0 0 0 0 0 3.1 × 10^-4         	║  Every time we move the decimal left, we add 1 to the power  ║
                                ║       So, we have to move the decimal left by ‘4’ places     ║
                                ║                 to get this power up to zero                 ║
So, the number becomes:         ╙——————————————————————————————————————————————————————————————╜
         
         
  0 0.0 0 0 3.1 × 10⁰   =    0.00031 
     ▲ ▲ ▲ ▲ │ 
     └─└─└─└─┘ 
moving the decimal
left by 4 places

b) Convert each of these numbers from Standard Index Form to ordinary numbers (Full Digital Form):

i) \(2.12\times 10^4\)

ii) \(6\times 10^3\)

iii) \(1.4\times 10^{-3}\)

Hints

Part (i):

Write the number as:                      2.1 2 0 0 0 0 0 × 10⁴ 
Then, knock 1 off the power and            └─┐                ⭭
move the decimal RIGHT by 1 place:        2 1.2 0 0 0 0 0 × 10³ 
                                             └─┐              ⭭
                                          2 1 2.0 0 0 0 0 × 10² 
                                               └─┐            ⭭
                                          2 1 2 0.0 0 0 0 × 10¹ 
                                                 └─┐          ⭭
                                          2 1 2 0 0.0 0 0 × 10⁰ 
        
And then cross out the × 10⁰   	=         2 1 2 0 0.0 0 0
        
                                =         2 1 2 0 0

Hints

Part (ii):

Write the number as: 6.00000 × 10³, then move the decimal RIGHT by �places

Hints

Part (iii):

Write the number as: 000001.4 × 10^-3, then move the decimal LEFT by �places

c) Convert these numbers from Standard Index Form to ordinary numbers (Full Digital Form):

i) \(8.23\times 10^3\)

ii) \(5\times 10^5\)

iii) \(2.1\times 10^{-4}\)

Hints

Part (i): You need to manage this all by yourself

Hints

Part (ii): Sorry: No hints for this

Hints

Part (iii): Sorry! 🤭

If you failed Question 2 in the test, you must do these 3 extra questions:

a) Re-write the following numbers in Standard Index Form:

i) \(1234.56\)

ii) \(12,000\)

iii) \(0.00123\)

Hints

Part (i):

Start by writing the number as:
         
  1 2 3 4.5 6 × 10⁰ 
         
Now move the decimal until there is just 1 digit in-front of it (this digit cannot be a zero):
         
                  ╔═════════════╗
                  ▼             ╟—————————————————————————————————————————————————————————————╖
  1 2 3 4.5 6 × 10⁰           	║ Every place we move the decimal left, we add 1 to the power ║
       ┌─┘        ⭭             ╙—————————————————————————————————————————————————————————————╜
  1 2 3.4 5 6 × 10¹ 
     ┌─┘          ⭭
  1 2.3 4 5 6 × 10² 
   ┌─┘            ⭭
  1.2 3 4 5 6 × 10³    =    1.23456 × 10³ 
▲
│ ┌──────────────────────┐
└─┤ Until there is only  │
  │  1-digit in-front    │
  │ of the decimal-point │
  └──────────────────────┘

Hints

Part (ii):

Start by writing the number as:
         
1 2 0 0 0.0 × 10⁰ 
         
Now move the decimal until there is just 1 digit in-front of it (this digit cannot be a zero):
         
                  ╔═════════════╗
                  ▼             ╟——————————————————————————————————————————————————————————————╖
  1 2 0 0 0.0 × 10⁰            	║  Every place we move the decimal left, we add 1 to the power ║
         ┌─┘      ⭭             ╙——————————————————————————————————————————————————————————————╜
  1 2 0 0.0 0 × 10¹ 
       ┌─┘        ⭭
  1 2 0.0 0 0 × 10² 
     ┌─┘          ⭭
  1 2.0 0 0 0 × 10³ 
   ┌─┘            ⭭
  1.2 0 0 0 0 × 10⁴    =    1.20000 × 10⁴    =    1.2 × 10⁴ 
  ▲
  │ ┌──────────────────────┐
  └─┤ Until there is only  │
    │  1-digit in-front    │
    │ of the decimal-point │
    └──────────────────────┘

Hints

iii) We can only add the powers if the bases are the same!

Start by writing the number as:
         
0.0 0 1 2 3 × 10⁰ 
         
Now move the decimal until there is just 1 digit in-front of it (this digit cannot be a zero):
         
                  ╔═════════════╗
                  ▼             ╟—————————————————————————————————————————————————————————————————╖
  0.0 0 1 2 3 × 10⁰            	║ Every place we move the decimal right, we knock 1 off the power ║
   └─┐            ⭭             ╙—————————————————————————————————————————————————————————————————╜
  0 0.0 1 2 3 × 10^-1 
     └─┐          ⭭
  0 0 0.1 2 3 × 10^-2 
       └─┐        ⭭
  0 0 0 1.2 3 × 10^-3    =    0001.23 × 10^-3    =    1.23 × 10^-3 
  ⭫ ⭫ ⭫  ▲
  These  │ ┌──────────────────────────┐
  zeros‹┐└─┤ Until there is only ‘1’  │
  don't └──┼›(non-zero)-digit in-front│
  count    │ of the decimal-point     │
           └──────────────────────────┘

b) Re-write the following numbers in Standard Index Form:

i) \(123.456\)

ii) \(1,200,000\)

iii) \(0.0123\)

Hints

Part (i):

Write the number as:                         1 2 3.4 5 6 × 10⁰ 
Then, move the decimal left 1 place             ┌─┘          ⭭
and add '1' to the power:                    1 2.3 4 5 6 × 10¹ 
                                              ┌─┘            ⭭
                                             1.2 3 4 5 6 × 10²

Hints

Part (ii):

Part (ii):
         
Write as: 1,200,000.0 × 10⁰, then move the decimal LEFT by � places and add �to the power

Hints

Part (iii):

Part (iii):
         
Write as: 0.0123 × 10⁰, then move the decimal RIGHT by � places and knock � off the power

c) Convert the numbers below into Standard Index Form:

i) \(12.3456\)

ii) \(120\)

iii) \(0.00000123\)

Hints

You need to answer these three without my help…

                                    …but they are worked out in exactly the same way as Part (b)

If you failed Question 3 in the test, you must do these 3 extra questions:

a) If \(a=1.25\times 10^5\) and \(b=4.5\times 10^3\), find, in Standard Index Form:

i) \(a+b\)

ii) \(a-b\)

iii) \(a+3b\)

Hints

i) An ‘^¹⁄₂’ in the power means ²√
(square-root: usually just written as ²√ )

We can only add numbers in standard form, if the exponents are the same…
         
We need to convert  the one with the lower power:
                   └───────────────────────┬─────┘
                                           ‎‏˅
                   1.25 × 10⁵   +   4.5 × 10³ 
                                   ╘════╤════╛ 
                               ┌────────┴────────┐   ╒══════════════════════════════════════╕
                               │So convert this ═╪═══╪═► move the decimal left (increasing	│
                               └────────┬────────┘   │ the power by 1 with each move) until	│
                               ┌────────┴────────┐   │ it matches the power of the other №	│
                               │ now add them ◄══╪═══╪═0.045 × 10⁵ ⇐ 0.45 × 10⁴ ⇐ 4.5 × 10³	│
                               └────────┬────────┘   ╘══════════════════════════════════════╛
                                   ╒════╧══════╕
                   1.25 × 10⁵   +    0.045 × 10⁵ 
                  └──┬─┘           └─┬───┘    
                     └─────ADD─────┬─┘        
                                ┌──┴──┐  
                                 1.295   × 10⁵

Hints

Part (ii):

Start by working out                                3b:	
                      a	=  1.25 × 10⁵          	     b	=   4.5 × 10³ 
                                                    3b	= 3×4.5 × 10³  
                                                         └──┬──┘
                                                         ┌──┴─┐
                                                    3b=   13.5  × 10³
         
         
NOW
make the powers the same:  1.25 × 10⁵   -   13.5 × 10³ 
                                          ╘═════╤════╛ 
                                       ┌────────┴────────┐
                                        convert this one:
                                       └────────┬────────┘
                                       ╒════════╧═══════════════════════════════╕
                                        move the decimal to the left (increasing
                                        the power by 1 with each move) until the
                                        power is the same as the other number:
                                        13.5 × 10³  =  1.35 × 10⁴  =  0.135 × 10⁵ 
                                       ╘════════╤══════════════════════════════╛
                                       ┌────────┴─────────┐
                                        now subtract them:
                                       └────────┬─────────┘
                                          ╒═════╧═════╕
                           1.25 × 10⁵  -    0.135 × 10⁵ 
         
             =                 ...  × 10⁵ 
		
BUT, this ain't is Standard Index Form

You need to shift the decimal until there is only 1 (non-zero) digit to the left of it...
(and adjust the exponent accordingly!)

Hints

Part (iii):

We can only subtract numbers in standard form, if the exponents are the same…
         
We need to convert  the one with the lower power:
                   └───────────────────────┬─────┘
                                           ‎‏˅
                   1.25 × 10⁵   -   4.5 × 10³ 
                                   ╘════╤════╛ 
                               ┌────────┴────────┐   ╒══════════════════════════════════════╕
                               │So convert this ═╪═══╪═► move the decimal left (increasing	│
                               └────────┬────────┘   │ the power by 1 with each move) until	│
                               ┌────────┴────────┐   │ it matches the power of the other №	│
                               │ now add them ◄══╪═══╪═0.045 × 10⁵ ⇐ 0.45 × 10⁴ ⇐ 4.5 × 10³	│
                               └────────┬────────┘   ╘══════════════════════════════════════╛
                                   ╒════╧══════╕
                   1.25 × 10⁵   +    0.045 × 10⁵ 
                  └──┬─┘           └─┬───┘    
                     └───SUBTRACT──┬─┘        
                                ┌──┴──┐  
                                 1.205  × 10⁵

b) If \(p=4.5\times 10^6\) and \(q=5\times 10^5\), find, in Standard Form:

i) \(p+q\)

ii) \(p-q\)

iii) \(3p-\frac{3}{2}q\)

Hints

Part (i):

ALLs wez gotz'ta do is ADD EM UP:
	
Start by re-writing the one with the lower power:
                   └─────────────────────┬───────┘
                                         ‎‏˅
                   4.5 × 10⁶    +   5 × 10⁵ 
                                   ╘════╤════╛ 
                               ┌────────┴────────┐   ╒══════════════════════════════════════╕
                               │So convert this ═╪═══╪═► move the decimal left (increasing	│
                               └────────┬────────┘   │ the power by 1 with each move) until	│
                               ┌────────┴────────┐   │ it matches the power of the other №	│
                               │ now add them ◄══╪═══╪═ 0.50 × 10⁶  ⇐   5.0 × 10⁵         	│
                               └────────┬────────┘   ╘══════════════════════════════════════╛
                                   ╒════╧════╕
                   4.5 × 10⁶    +    0.5 × 10⁶ 
         
             =                ...  × 10⁶

Hints

Part (ii):

We juz needz to SUBTRACTZ 'em:
          
Start by re-writing the one with the smaller exponent:
         
                   4.5 × 10⁶    -   5 × 10⁵ 
                                   ╘═══╤═══╛ 
                              ┌────────┴────────┐
                               convert this one:
                              └────────┬────────┘
                              ╒════════╧═══════════════════════════════╕
                               move the decimal to the left (increasing
                               the power by 1 with each move) until the
                               power is the same as the other number:
                                       5.0 × 10⁵   =   0.50 × 10⁶  
                              ╘════════╤══════════════════════════════╛
                             ┌─────────┴─────────┐
                              now we can add them:
                             └─────────┬─────────┘
                                   ╒═══╧═════╕
                    4.5 × 10⁶    -   0.5 × 10⁶ 
         
             =                 ...  × 10⁶

Hints

Part (iii):

Start by working out 3p:         and          	   ³⁄₂q:
                     ------------------------------------------------	
                      p	=   4.5 × 10⁶          	      q	=     5 × 10⁵ 
                     3p	= 3×4.5 × 10⁶         	   ³⁄₂q	= ³⁄₂×5 × 10⁵  
                         └──┬──┘                         └──┬──┘
                          ┌─┴──┐                          ┌─┴─┐
                     3p	=  13.5   × 10⁶       	   ³⁄₂q =  7.5  × 10⁵
         
         
NOW
make the powers the same:  13.5 × 10⁶   -   7.5 × 10⁵ 
                                           ╘════╤═══╛ 
                                       ┌────────┴────────┐
                                        convert this one:
                                       └────────┬────────┘
                                       ╒════════╧═══════════════════════════════╕
                                        move the decimal to the left (increasing
                                        the power by 1 with each move) until the
                                        power is the same as the other number:
                                                7.5 × 10⁵   =   0.75 × 10⁶  
                                       ╘════════╤═══════════════════════════════╛
                                       ┌────────┴─────────┐
                                        now subtract them:
                                       └────────┬─────────┘
                                           ╒════╧═════╕
                           13.5 × 10⁶   -    0.75 × 10⁶ 
         
             =                      ...  × 10⁶ 
		
BUT, this ain't is Standard Index Form

You need to shift the decimal until there is only 1 (non-zero) digit to the left of it…
(and adjust the exponent accordingly!)

c) If \(x=7.2\times 10^8\) and \(y=5\times 10^6\), find, in Standard Form:

i) \(x+2y\)

ii) \(2x-3y\)

iii) \(\frac{1}{3}x-\frac{3}{4}y\)

Hints

Clue: Sorry, noooo mooore help…

If you failed Question 4 in the test, you must do these 3 extra questions:

a) If \(a=1.5\times 10^9\) and \(b=3\times 10^6\), find in Standard Form, the values of:

i) \(ab\)

ii) \(\frac{a}{b}\)

iii) \(b^3\)

Hints

Part (i):

We want to find: 1.5 × 10⁹  ×  3 × 10⁶ 
         
                         ╔═══════════╦════╗
                         ▼           ▼    ║
                 1.5 × 10⁹  ×  3 × 10⁶    add
                └─┬─┘         └┬┘     ╔═══╝
                  └─multiply─┬─┘      ║    
                           ┌─┴─┐      ▼
                            4.5  ×  10¹⁵

Hints

Part (ii):

Part (ii):
         
We want to find: 1.5 × 10⁹  ÷ 3 × 10⁶         
         
                       ╔═══════════╦══════╗
                       ▼           ▼      ║
                 1.5 × 10⁹  ?  3 × 10⁶  subtract
                └─┬─┘         └┬┘     ╔═══╝
                  └──divide──┬─┘      ║    
                           ┌─┴──┐     ▼
                            0.5   ×  10³ 
                           ╘═════╤══════╛ 
                    ┌────────────┴────────────┐   ╒═══════════════════════════════════════╕
                    │this isn't standard form:╪═══╪► move the decimal 1 place to the RIGHT│
                    └────────────┬────────────┘   │so there's just ONE (non-zero) digit to│
                    ┌────────────┴────────────┐   │the left of it. Knock ‘1’ off the power│
                    │so the final answer is ◄═╪═══╪═    5.0 × 10^?  ⇐  0.50 × 10³          	│
                    └────────────┬────────────┘   ╘═══════════════════════════════════════╛
                            ╒════╧════╕
                              5  × 10^?

Hints

Part (iii):

                                 3
We want to find:     ⎧ 3 × 10₆ 	⎫ 
                     ⎩       	⎭
 

We can DISTRIBUTE THE POWER (into the bracket)
 
                                3
                     ⎧ 3 × 10₆ 	⎫    =   3³ × (10₆)³  
                     ⎩       	⎭       └┬┘  └──┬──┘
                                         │      └────────────── This is just: 10¹⁸  
            this is ‘27’ ────────────────┘                      (i.e. multiply the powers)
 
	
BUT, this ain't is Standard Index Form

You need to shift the decimal until there is only 1 (non-zero) digit to the left of it…
(and adjust the exponent accordingly!)

b)If \(p=4.5\times 10^4\) and \(q=3\times 10^2\), find:

i) \(pq\)

ii) \(p\div q\)

iii) \(\frac{p}{q^2}\)

Hints

Part (i):

We want to find: (4.5 × 10⁴) × (3 × 10²)        => ...  × 10^? 
         
                          ╔═══════════╦════╗
                          ▼           ▼    ║
                  4.5 × 10⁴  ×  3 × 10²    add
                 └─┬─┘         └┬┘     ╔═══╝
                   └─multiply─┬─┘      ║   
                            ┌─┴──┐     ▼
                             13.5 ×  10⁶ 
                           ╘═════╤══════╛ 
                    ┌────────────┴────────────┐   ╒═══════════════════════════════════════╕
                    │this isn't standard form:╪═══╪► move the decimal 1 place to the LEFT │
                    └────────────┬────────────┘   │  so there's just ONE (non-zero) digit │
                    ┌────────────┴────────────┐   │  in-front of it. Add ‘1’ to the power │
                    │so the final answer is ◄═╪═══╪═    1.35 × 10^? ⇐  13.5 × 10⁶        	│
                    └────────────┬────────────┘   ╘═══════════════════════════════════════╛

Hints

Part (ii):

We want to find: (4.5 × 10⁴) ?÷(3 × 10²)        => ... × 10^? 
         
Dividing the numbers gives:                    => ... × 10^? 
   
SUBTRACTING the exponents gives:               => ... × 10² 
         
Which is the answer!

Hints

Part (iii): Sorry matey; you get nothing from me!

c) Given \(u=4\times 10^6\) and \(v=8\times 10^5\), calculate the following, giving your answers in Standard Form

i) \(\sqrt{u}\)

ii) \(\frac{uv^2}{100}\)

iii) \(\frac{u+v}{\sqrt[3]{2u}}\)

Hints

Part (i):

We want to find √u, which is actually the same as: u^½ (although we don't need to know that to answer this)
 
       √u   =  √4 × 10⁶  
 
            =  √4  × √10⁶  
 	
            =  √4  × √1,000,000  
              └─┬─┘ └─────┬─────┘
Everyone        │         └──────────────── I'm pretty sure you can guess this!
knows this  ────┘
   
 
Don't forget to put your answer BACK into Standard Index Form

Hints

Part (ii): I would if I could, but I can't so I shan't...

Hints

Part (iii): I'm sorry, but you are all alone now.

If you failed Question 5 in the test, you must do these 3 extra questions:

a) A litre mineral water contains \(1.25\times 10^5\) mineral particles.

A litre of tap water contains \(4.5\times 10^3\) particles of tap water.

If these two are mixed, how many mineral particles will be in the two litres of mixed water?

Hints

So, really, all we gotsta do is just ADD: 1.25 × 10⁵  +  4.5 × 10³ 
         
(If you are stuck on how to add them, then see the hints for Question 3)

b) It is estimated that an eruption of the volcano on Mount Rinjani (Indonesia) would kill \(5\times 10^5\) people.

New, early warning systems should reduce the death toll by 40%

Given the population of Indonesia is \(4.5\times 10^6\), how many people would be left, if the early warning system was employed.

Hints

Clue:
                                 ┌────────────────── Let D = death toll (no warning ?) 
                                 ▼
Without Early Warning System:    D = 5 × 10⁵  
 
But, with the Warning System:   ⅗D = .....
 
Then, we need to subtract
         
[If you are stuck on how to subtract them, then see the hints for Question 3]

c) A space probe travels at the speed of light (\(3\times 10^8\) m/s).

It is fired from the Earth towards the Sun, a distance of \(1.5\times 10^9\) metres.

How long will the journey take in seconds?

Hints

Use:      Speed  =  distance              =>              time  =  distance
                      time                                           speed

Good Luck! ☘

a) Convert each of these three numbers from Standard Index Form to ordinary numbers (Full Numerical Form):

i) \(2.236\times 10^3\)

ii) \(4.3\times 10^4\)

iii) \(3.1\times 10^{-4}\)

b) Convert each of these numbers from Standard Index Form to ordinary numbers (Full Digital Form):

i) \(2.12\times 10^4\)

ii) \(6\times 10^3\)

iii) \(1.4\times 10^{-3}\)

c) Convert these numbers from Standard Index Form to ordinary numbers (Full Digital Form):

i) \(8.23\times 10^3\)

ii) \(5\times 10^5\)

iii) \(2.1\times 10^{-4}\)

a) Re-write the following numbers in Standard Index Form:

i) \(1234.56\)

ii) \(12,000\)

iii) \(0.00123\)

b) Re-write the following numbers in Standard Index Form:

i) \(123.456\)

ii) \(1,200,000\)

iii) \(0.0123\)

c) Convert the numbers below into Standard Index Form:

i) \(12.3456\)

ii) \(120\)

iii) \(0.00000123\)

a) If \(a=1.25\times 10^5\) and \(b=4.5\times 10^3\), find, in Standard Index Form:

i) \(a+b\)

ii) \(a-b\)

iii) \(a+3b\)

b) If \(p=4.5\times 10^6\) and \(q=5\times 10^5\), find, in Standard Form:

i) \(p+q\)

ii) \(p-q\)

iii) \(3p-\frac{3}{2}q\)

c) If \(x=7.2\times 10^8\) and \(y=5\times 10^6\), find, in Standard Form:

i) \(x+2y\)

ii) \(2x-3y\)

iii) \(\frac{1}{3}x-\frac{3}{4}y\)

a) If \(a=1.5\times 10^9\) and \(b=3\times 10^6\), find in Standard Form, the values of:

i) \(ab\)

ii) \(\frac{a}{b}\)

iii) \(b^3\)

b)If \(p=4.5\times 10^4\) and \(q=3\times 10^2\), find:

i) \(pq\)

ii) \(p\div q\)

iii) \(\frac{p}{q^2}\)

c) Given \(u=4\times 10^6\) and \(v=8\times 10^5\), calculate the following, giving your answers in Standard Form

i) \(\sqrt{u}\)

ii) \(\frac{uv^2}{100}\)

iii) \(\frac{u+v}{\sqrt[3]{2u}}\)

a) A litre mineral water contains \(1.25\times 10^5\) mineral particles.

A litre of tap water contains \(4.5\times 10^3\) particles of tap water.

If these two are mixed, how many mineral particles will be in the two litres of mixed water?

b) It is estimated that an eruption of the volcano on Mount Rinjani (Indonesia) would kill \(5\times 10^5\) people.

New, early warning systems should reduce the death toll by 40%

Given the population of Indonesia is \(4.5\times 10^6\), how many people would be left, if the early warning system was employed.

c) A space probe travels at the speed of light (\(3\times 10^8\) m/s).

It is fired from the Earth towards the Sun, a distance of \(1.5\times 10^9\) metres.

How long will the journey take in seconds?

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