This preview shows page 1. Sign up to view the full content.
Unformatted text preview: t having any
c2
fractions in your final answer.
If a = b 3 and b = 3.4 Standard Form
Standard form is a convenient way of writing very large or very small numbers.
It is used on a scientific calculator when a number is too large or too small to be
displayed on the screen.
Before using standard form, we revise multiplying and dividing by powers
of 10. Example 1
Calculate:
(a) 3 × 10 4 (b) 3.27 × 10 3 (c) 3 ÷ 10 2 (d) 4.32 ÷ 10 4 Solution
(a) 3 × 10 4 = 3 × 10 000
= 30 000 (b) 3.27 × 10 3 = 3.27 × 1000
= 3270 (c) 3 ÷ 10 2 = 3
100 = 0.03 49 MEP Y9 Practice Book A 3.4
(d) 4.32 ÷ 10 4 =
= 4.32
10 000
432
1000 000 = 0.000432
These examples lead to the approach used for standard form, which is a reversal
of the approach used in Example 1.
In standard form, numbers are written as a × 10 n
where 1 ≤ a < 10 and n is an integer. Example 2
Write the following numbers in standard form:
(a) 5720 (b) 7.4 (c) 473 000 (d) 6 000 000 (e) 0.09 (f) 0.000621 Solution
(a) 5720 = 5.72 × 1000
= 5.72 × 10 3 (b) 7.4 = 7.4 × 1
= 7.4 × 10 0 (c) 473 000 = 4.73 × 100 000
= 4.73 × 10 5 (d) 6 000 000 = 6 × 1000 000
= 6 × 10 6 (e) 0.09 = 9
100 = 9 ÷ 10 2
= 9 × 10 − 2 50 MEP Y9 Practice Book A (f) 0.000621 =
= 6.21
10 000
6.21
10 4 = 6.21 × 10 − 4 Example 3
Calculate:
(a) (3 × 10 ) × (4 × 10 ) (b) (6 × 10 ) ÷ (5 × 10 ) (c) (3 × 10 ) + (2 × 10 ) 6 7 4 3 −2 5 Solution
(a) (3 × 10 ) × (4 × 10 )
6 3 = (3 × 4) × (10 6 × 10 3 )
= 12 × 10 9
= 1.2 × 10 1 × 10 9
= 1.2 × 10 10 (b) (6 × 10 ) ÷ (5 × 10 )
7 −2 = (6 ÷ 5) × (10 7 ÷ 10 − 2 )
= 1.2 × 10 9 (c) (3 × 10 ) + (2 × 10 )
4 5 = 30 000 + 200 000
= 230 000
= 2.3 × 10 5 Note on Using Calculators
Your calculator will have a key
form. EE or EXP for entering numbers in standard For example, for 3.2 × 10 7 , press
3 . 2 51 EXP 7 MEP Y9 Practice Book A 3.4 which will appear on your display like this: 3.2 07 Some calculators also display the ' × 10 ' part of the number, but not all do. You
need to find out what your calculator dis...
View Full
Document
 Fall '13
 Zeeshan

Click to edit the document details