Student Exercises
1.
Basic number exercises
(i)
Write out the number 101,280.37 in words
(ii)
Write out the number 4.0E 6 in words
(iii)
Write out the number 3.7E 3 in words
(iv)
Write seventy three point zero seven eight as a number
(v)
Write one millionth as a number in scientific notation
(vi)
Write 1,730,000 as a number in scientific notation
(vii)
Write the number 8 in binary notation
(viii) Write the number 39 in binary notation
(ix)
Write the binary number 1110 in decimal notation
(x)
Write the hexadecimal number 2Cin decimal notation
Answer Guidelines
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
One hundred and one thousand, two hundred and eighty point three seven
Four million [or four times ten to the power six]
Three thousand seven hundred [or three point seven times ten cubed].
73.078
1E -6
1.73E 6 (or 17.3E5, 173E4 etc)
1000 (i.e. 1x23 + 0x22 + 0x21 +0x20)
100111 (i.e. 1x25 + 0x24 + 0x23 1x22 + 1x21 + 1x20 = 32+4+2+1)
14 (i.e. 1x23 + 1x22 + 1x21 +0x20 = 8+4+2)
44 (i.e. 2x161 + 12x160 = 32+12)
2.
Basic arithmetic exercises: calculate the following:
(i)
(1+4)x(3+2)
(ii)
32+4
(iii)
(-2)x4
(iv)
(-2)x(2-3)
(v)
3(12-8)
(vi)
2.666 rounded to the nearest whole number
(vii)
2.666 rounded to 1 decimal place
(viii) 2.666 truncated to a whole number
(ix)
2.666 truncated to 1 decimal place
(x)
The approximate number of spanners produced by a factory in a week (42 hours)
with 20 machines each producing 29 spanners per hour. Use estimation.
Answer Guidelines
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(1+4)x(3x2) = 5x5 =25
32+4 = 9+4 = 13
(-2)x4 = -(2x4) = -8
(-2)x(2-3) = (-2)x(-1) = 2
3(12-8) = 3x4 = 12
2.666 rounded to the nearest whole number = 3
2.666 rounded to 1 decimal place = 2.7
2.666 truncated to a whole number = 2
2.666 truncated to 1 decimal place = 2.6
(x)
Using estimation, 42x20x29 ≈ 40x20x30 = 24,000 [the correct number is
42x20x29 = 24,360]
3.
Powers, roots and logs: calculate the following:
(i)
23+22
(ii)
23–22
(iii)
23x22
(iv)
23/22
(v)
3-2x33
(vi)
3(-2)
(vii)
6(-3) x62
(viii) 3(-3)/3
(ix)
Log2(32)
(x)
log10(24) [Note: log10(2 ) = 0.301]
Answer Guidelines
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
(ix)
(x)
23+22 = 8+4 =12
23–22 = 8-4 = 4
23x22 = 2(3+2) = 25 = 32
23/22 = 2(3-2) = 21 = 2
3-2x33 = 3(-2+3) = 31 = 3 [or 3-2x33 = (1/9)x27 = 27/9 = 3]
3(-2) = 1/32 = 1/9 = 0.111
6(-3) x62 = 6(-3+2) = 6(-1) = 1/6 = 0.178
3(-3)/3 = 3(-3-1) = 3(-4) = 1/34 = 1/81 = 0.012
Log2(32) = log2(25) = 5log2(2) = 5x1 = 5
log10(24) = 4log(2) = 4x0.301 = 1.204
4.
A trader buys 20 goods for £5.00 each plus commission at 10%. She then sells on the
goods with a 40% mark up. She has to pay 25% tax on her profits. How much tax does she
pay?
Answer Guidelines
Total amount spent before commission = 20x£5.00 = £100.00
Commission at 10% = £100.00x10/100 = £10.00
Total amount spent on the goods = £100.00+£10.00 = £110.00
40% mark up on £110.00 = £110.00x40/100 = £44.00
Total selling price for the 10 goods = £110.00+£44.00 = £154.00
Total profit = £154.00-£110.00 = £44.00
25% Tax on £44.00 profit = £44.00x25/100 = £11.00
Answer = £11.00
5.
A company buys a machine in America for $3,000.00 and pays $1,000.00 dollars to have it
transported to Europe. The company then sells the machine in Greece. What must the
company charge the Greek customer in order to make 100% profit on costs? Assume that
the exchange rate between US dollars and sterling is $1=£0.60, that the exchange rate
between sterling and Euros is £1= €1.50, and ignore the effect of taxes.
Answer Guidelines
Total cost of the machine and transport = $3,000.00+$1,000.00 = $4,000.00
Total cost of the machine and transport in sterling = 4,000x£0.60 = £2,400.00
Total cost of the machine and transport in euros = 2,400x€1.50 = €3,600.00
In order to make 100% profit, the company must sell the machine for €7,200.00
Answer €7,200.00