CONVERTING NUMBERS
TO
STANDARD FORM
Introduction
Standard Form (Standard Index Form)
For VERY BIG or VERY SMALL numbers.
e.g. 62,000,000,000 becomes 6.2 x 1010
0.0000000528 becomes 5.28 x 10-8
Standard Index Form
Ax
Integer
between
1 and 9
n
10
Multiplying by 10
“moves” the
Decimal Point, n is
the number of
moves (+ or -) ....
Powers of 10 are Positive or Negative
Standard Form uses both Multiplication and
Division by 10 by using powers.
Division by 10 is the same as Multiplying by
10-1 . Division by 100 (10 x 10) is the same as
Multiplying by 10-2 ..... and so on
0.034 x 102 = 3.4
3.4 x 10-2 = 0.034
Warm-Up - Rewrite As Normal Decimals
1) 46.34 x 102 =
2) 46.34 x 10-2 =
3) 37 x 105 =
4) 37 x 10-5 =
Answers
1) 46.34 x 102 = 4,634
2) 46.34 x 10-2 = 0.4634
3) 37 x 105
= 3,700,000
4) 37 x 10-5
= 0.00037
Standard Form Questions
Standard Form: A x 10n
Put the following numbers into Standard Form
1) 4733
4) 0.00000081
2) 0.00765
5) 7277.66
3) 932222
6) 0.000 000 000 0004
Answers To Standard Form
Standard Form: A x 10n
Put the following numbers into Standard Form
1) 4733
4) 0.00000081
4.733 x 103
8.1 x 10-7
1) 0.00765
5) 7277.66
7.65 x 10-3
7.27766 x 103
1) 932222
6) 0.000 000 000 0004
9.32222 x 105
4 x 10-13
SUMMARY
• Standard Form or Standard Index Form is a
way of handling VERY BIG or SMALL numbers
• A x 10n A is an integer between 1 and 9, n is a
positive or negative power of 10
• If you study Science at higher levels you will
see a lot of Standard Form numbers