Rounding Numbers – Part 2
Slideshow 2, Mr Richard Sasaki, Room
307
Objectives
• Understand the meaning of significant
figures
• Be able to write large or small numbers in
standard index form
• Be able to round and calculate with such
numbers
Rounding
Let’s have a quick review.
Round the number 74.752 to…
The nearest 2 decimal places
74.75
The nearest 1 decimal place
74.8
The nearest integer
75
This is a common way to round numbers with
decimals. Next we’ll look at rounding with
significant figures.
Significant Figures
If we see a number like 4,458,327,732 it doesn’t
look very nice. It may be that some of those digits
aren’t very significant so we can simplify it a bit.
When we found a number to __ significant figures,
we rewrite that number to only show interest in
those figures.
Examples
Write 347 rounded to 2 significant figures.
350
Write 75,321 rounded to 3 significant
figures.
75,300
Significant Figures
We can also do this with small decimal numbers.
Examples
Write 5.329 rounded to 3 significant figures. 5.33
Write 0.00593 rounded to 1 significant
0.006
figure.
Any zeroes at the start or end of big or small
numbers do not count towards significant digits.
53,000,000
(2 s.f)
0.0005003
(4 s.f)
Answers
4
428,000
430,000
400,000
6
0.00048232
0.000482
0.0005
9.392
9.4
9
837.2
50.00
45.50
100.00
840
50
45
100
800
50
50
100
483900480000500000
27360 27000 30000
124000120000100000
Standard Form
Standard (index) form comes from index form. If
we write a number in index form, we write it in the
form…
𝑏
𝑎
Writing numbers in standard form is very useful
and important for huge or tiny numbers. You will
see numbers in this style in physics and social
studies too.
But what is it?
Standard Form
To write a number in standard form, we split it into
two components.
I’ll use the number 741,200,000,000 for the
example.
11
7.412 × 10
This number contains all
significant figures. It
always has the units
figure on the left!
This number is always in
the form 10𝑥 where 𝑥 is
the number of digits –1.
Examples
Let’s write the following in standard form.
3,500,000,000
3.5 × 109
74,000,000,000
7.4 × 1010
82
8.2 × 101
7,530
7.53 × 103
0.004
4 × 10−3
0.00392
Try the worksheet!
3.92 × 10−3
Answers
4 × 103
3.59 × 104
5 × 106
4.92 × 105
3 × 10−2
8 × 10−4
5.79 × 10−3
5.43 × 100
9.43 × 104
9.65 × 107
1.5 × 106
9.75 × 100
−2
3.12 × 10
7 × 10−4
5.09 × 10−4
1 × 10−2
1.496 × 108
3 × 108
Answers
300
430,000
10
4.3
0.03
0.000043
0.1
0.48
7 × 103
9.3 × 10−8
7.3 × 107
4 × 102
8.42 × 103
3 × 102
9 × 103
1.13 × 108
5.2 × 103
4.20033 × 107
6.9 × 109
3.8 × 10−4
2.163 × 106
3.1 × 10−8