Chapter 11 Exponential And Logarithmic Relations - 11f. Standard Form Worksheet
ADVERTISEMENT
1
2Standard form
11F
Scientists use standard form or scientific notation to write very large and very small numbers.
A number in scientific notation takes the form a × 10
p
where:
a
is a decimal number between 1 and 10
p
is either a positive or negative integer (whole number).
Example
Solution
1
The distance of the planet Pluto from the
Shift the decimal point nine places to the left:
Sun is 5 900 000 000 km. Write this in
5 900 000 000· = 5·9 × 10
9
km
standard form.
2
Write 8·45 × 10
6
as a basic numeral.
Shift the decimal point six places to the right:
8·45 × 10
6
= 8·450 000 = 8 450 000
3
Write the diameter of an atom, which is
Shift the decimal point seven places to
0·000 000 1 millimetres, as a standard
the right:
form number.
0·000 000 1 = 1·0 × 10
–7
mm
4
Write 4·25 × 10
–4
as a basic numeral.
Shift the decimal point four places to the left:
4·25 × 10
–4
= 00 004·25 = 0·000 425
A TI-89 calculator can be used to work with large numbers in
standard form.
5·9 × 10
9
= 5 900 000 000
8·45 × 10
6
= 8 450 000
If a result cannot be displayed in the number of digits specified
in Display Digits of the MODE menu, then standard form is
used in which E represents the power of 10.
1·0 × 10
–7
= 0·000 000 1
The results displayed are:
1
Exact mode 1·0 × 10
=
–7
------------------------- -
10 000 000
Approximate mode 1·0 × 10
= 1·E
–7
–
7
Exercise 11F
1
Write the following basic numerals in standard form:
a
60 000
b
120 800
c
550
d
75 000 000
e
490 000
f
750
g
50
h
3·5
2
Write the following standard form numbers as basic numerals:
2·5 × 10
8·05 × 10
7·621 × 10
8·205 × 10
3
6
5
6
a
b
c
d
4·9 × 10
8
9·5 × 10
2
6·0 × 10
1
9·5 × 10
0
e
f
g
h
3
Write the following basic numerals in standard form:
a
b
c
d
0·006
0·001 08
0·75
0·000 625
e
0·5
f
0·000 000 6
g
0·000 002 5
h
0·000 061
359
Chapter 11 Exponential and Logarithmic Relations
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education