Download standard (index) form

N1-1c-SIForm.docx
STANDARD (INDEX) FORM
Watch the Higher GCSE Maths Videoclip called: Powers and Roots > Topic 23 > Part 1 > Standard Index Form
Standard (Index) Form is a way of writing very big or very small values by using this shorthand version:
A x 10
where 1 ≤ A < 10
n
and
(i.e. it is between 1 and 10)
n = positive for big numbers
n = negative for small numbers
These numbers ARE in standard form:
3.6 x 107
or
4.02 x 10–4
These numbers are NOT in standard form:
23.6 x 10–2
or
0.8 x 103
(because A is bigger than 10!)
(because A is smaller than 1!)
To write standard form you find your ‘A’ value by writing the original value out with a decimal point after the
first non-zero digit. You then find your ‘n’ value by counting how many decimal places the point has moved in the
original value to make your ‘A’ value.
E.g. 420 000
 4.2  workings
4 2 0 0 0 0 .  point moves 5 places  420 000 = 4.2 x 105
E.g. 0.0105
 1.05  workings 0 . 0 1 0 5  point moves 2 places  0.0105 = 1.05 x 10–2
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N1-1c-SIForm.docx
Practice: Write these values in standard index form.
1)
92 000 = …………………………………………………
6)
0.004 = ……………………………………………………
2)
1 034 000 = ……………………………………………
7)
0.13 = ………………………………………………………
3)
14500 = …………………………………………………
8)
0.0000607 = …………………………………………
4)
88 = …………………………………………………………
9)
3 thousandths = ……………………………………
5)
12 million = ……………………………………………
10)
7.2 = …………………………………………………………
Save and complete the worksheet called: SIF-S2.xlsx
To evaluate standard form start from your ‘A’ value and use the ‘n’ value to move the decimal point the required
number of places to get back to the original value.
E.g. 6.4 x 103
 workings
E.g. 7.21 x 10–4  workings
6.4 0 0
 6.4 x 103 = 6400
0 0 0 0 7.2 1
 7.21 x 10–4 = 0.000721
Practice: Write these standard index form values out in full, i.e. evaluate them.
1)
5 x 102 = ……………………………………………………
6)
9 x 10–6 = ………………………………………………………
2)
3.12 x 104 = ………………………………………………
7)
6.07 x 10–2 = …………………………………………………
3)
8.36 x 105 = ………………………………………………
8)
5.64 x 10–3 = …………………………………………………
4)
7.2 x 101 = …………………………………………………
9)
9.004 x 10–1 = ………………………………………………
5)
4.8 x 100 = …………………………… ……………………
10)
1.17 x 10–2 = …………………………………………………
Save and complete the worksheet called: SIF-S4.xlsx
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N1-1c-SIForm.docx
When adding or subtracting with values in standard index form, you are advised to evaluate them first, add or subtract
them and then re-write your answer in standard index form (as/if required).
e.g. 5.6 x 103 + 2.89 x 104 
e.g.
5 6 0 0 + 2 8 9 0 0 = 3 4 5 0 0 = 3.45 x 104
7.0389 x 102 – 6.8 x 10–1  7 0 3 . 8 9 – 0 . 6 8 = 7 0 3 . 2 1 = 7.0321 x 102
When multiplying or dividing with values in standard form, you are advised to multiply or divide the A values together and
multiply or divide the powers of 10 together and then check the result is written in standard index form (as required),
i.e. that the A value is still between 1 and 10. If not, adjust the A and n values accordingly.
e.g.
4 x 105 x 4 x 102
 (4 x 4) x (105 x 102) =
16
x
105+2
 16 x 107 =
1.6 x 108
e.g.
7 x 103 ÷ 5 x 105
 (7 ÷ 5) x (103 ÷ 105) =
1.4
x
103-5

1.4 x 10-2
Of course if these sorts of questions come up on a calculator paper, you just need to know how to use YOUR calculator to
enter and evaluate standard index form.
Some calculators will represent answers in standard form by leaving a gap between the ‘A’ value and the ‘n’ value whilst
others have a tiny ‘x 10’ written in that gap.
So an answer of 3.7 x 104 might be displayed as:
or
x 10
To enter standard form values, many types of calculator have an EXP button. You type in your ‘A’ value followed by the
EXP button followed by the power of 10, i.e. the ‘n’ value.
e.g.
To calculate 1.3 x 10-1 + 3.247 x 102 you would press:
1
.
3
EXP
1
±
Work through the MyMaths lessons and their online homeworks called:
Number > Standard Form > Standard form large
& Standard form small
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+
&
3
.
2 4
7
EXP
Standard form calcs
2 =