Year 10 Standard Form - tandrageemaths
Standard Form
A number in Standard Form must be set out as follows:
3.2 x 104 OR 9.54 x 10-3 OR -2.3 x 1012
3.2 - the first number part must be between 1.0 and 9.99999999…
but it could be a minus number. E g. -4.6
x - the sign is always a times sign
104 - the base number is ALWAYS 10.
104 - the power number is ALWAYS a whole number, it may be positive,
negative OR even zero !
Key Points: 100 is the same as 1. 101 is the same as just 10.
Convert the following numbers into Standard Form
1) 26 500 2) 0.00823 3) 204 000 4) 0.05099
5) 0.00221 6) 1 070 030 7) 66.2 8) 4788
9) 0.000071 10) 89 000 11) 0.01 12) 0.00124
Convert the following numbers into ordinary numbers
1) 1.2 x 103 2) 3.14 x 10-2 3) 3.17 x 105 4) 9.55 x 10-3
5) 9.0704 x 105 6) 7.605 x 10-4 7) 1.15 x 10-6 8) 2.8 x 104
9) 2.63 x 106 10) 2.96 x 10-1 11) 8.45 x 103 12) 6.13 x 10-4
Convert the following non-standard form numbers into proper standard form
e.g. 23 x 102 is the same as 2.3 x 10 x 102 which is 2.3 x 103
0.34 x 10-2 is the same as 3.4 x 10-1 x 10-2 which is 3.4 x 10-3
Remember that dividing by 10 is the same as multiplying by 10-1. Dividing by 100 is the same as multiplying by 10-2, dividing by 1000 is the same as multiplying by 10-3 etc.
1) 12 x 103 2) 314 x 10-2 3) 0.317 x 105 4) 95.5 x 10-3
5) 9070.4 x 105 6) 7605 x 10-4 7) 0.0115 x 10-6 8) 0.0028 x 104
9) 26.3 x 106 10) 29.6 x 10-1 11) 845000 x 103 12) 0.00613 x 10-4
To multiply in standard form, multiply the number parts and then multiply the 10 parts, being careful to ADD the powers.
To divide in standard form, divide the number parts and then multiply the 10 parts, being careful to SUBTRACT the powers.
Using a calculator ONLY FOR THE NUMBER PART, work out the following. Write the answer as standard form.
1) (1.2 x 104) x (5.3 x 106) 2) (7.2 x 10-4) x (1.5 x 103)
3) (3.6 x 106) x (1.2 x 104) 4) (3.3 x 10-3) x (6.6 x 10-6)
5) (1.8 x 103) x (1.2 x 102) 6) (8.4 x 10-1) x (9.3 x 10-2)
7) (3.6 x 106) ÷ (1.2 x 104) 8) (8.4 x 104) ÷ (9.3 x 108)
9) (1.8 x 10-4) ÷ (1.2 x 108) 10) (8.4 x 10-1) ÷ (9.3 x 10-2)
To add and subtract in Standard Form, the power number for both parts MUST be the same.
e.g. 3.2 x 103 + 2.1 x 103 = 5.3 x 103 but
3.2 x 103 + 2.1 x 104 cannot be done. We must make both powers the same by making 3.2 x 103 equal to 0.32 x 104 OR 2.1 x 104 equal to 21 x 103.
Convert the following numbers so they have the same powers.
1) 4.0 x 103 , 3.0 x 102 (103) 2) 6.2 x 102 , 8.0 x 103 (103)
3) 1.7 x 105 , 3.2 x 104 (105) 4) 9.6 x 107 , 7.5 x 106
5) 5.2 x 10-2 , 4.8 x 10-1 (10-1) 6) 6.8 x 10-4 , 3.9 x 10-5
7) 3..9 x 10-1 , 1.1 x 100 8) 6.8 x 103 , 9.6 x 105
Add the pairs of numbers above in questions 1 – 8 and then calculate the following additions and subtractions, leaving the answers in correct standard form.
{remember, it is easiest to convert to the higher power}
1) (1.2 x 104) + (5.3 x 104) 2) (7.2 x 10-4) + (1.5 x 10-4)
3) (3.6 x 106) + (9.2 x 106) 4) (6.6 x 10-3) - (3.3 x 10-3)
5) (1.8 x 103) + (1.2 x 102) 6) (8.4 x 101) + (9.3 x 102)
7) (1.8 x 103) + (9.4 x 102) 8) (8.4 x 10-1) - (9.3 x 10-2)
9) (1.8 x 103) - (1.2 x 104) 10) (8.4 x 104) + (9.3 x 102)
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