Lesson
Degrees of Accuracy
Standard Form
1|P age
Lesson – Estimation and Standard Form
Objectives of the lesson
By the end of the lessoon we will:
Round numbers to differing degrees of accuracy
Estimate our answers
Understand how to represent a number in Standard Form
Calculate with Standard Form
2|P age
Lesson – Estimation and Standard Form
Degrees of Accuracy
What do we mean by degrees of accuracy? When we are giving answers sometime we
don’t want the entire answer
For instance, if I asked for the exchange rate of between pounds and euros the
exchange rate is an infinite decimal.
I would prefer the shortened version or one that is ‘rounded’.
We can commonly achieve this in 2 ways.
• Decimal Place
• Significant Figures
Decimal Places means that we round to the number of decimal places after the decimal
point (remember to round up if the final digit is 5 or above or to stay where it is if 4 or
below
Example
• 12.562 to 2 decimal places
This means that we want to stop our number 2 points after the decimal place.
12.562
i.e. between the 6 and the 2
• draw a box around the number to the immediate left and right of the dotted
line
• Round that number to the nearest 10
12.562
62 to the nearest 10 is 60
12.560
• Write your answer down, stopping 2 numbers after the decimal point
Answer: 12.56
3|P age
Lesson – Estimation and Standard Form
Make your own notes section! (group examples)
• 9.558 to 1 decimal place
Example 2
• Round 0.05961 to 1 s.f.
Significant figures questions are just like decimal places except rather than rounding
to an amount of numbers after a decimal point we round the amount of non –zero
digits from the start of the number.
In the number 0.05961 the first non-zero digit is the 5
0.05961
Rounding this number to the nearest 10:
59 -> 60
0.060
It says 1 significant figure so we stop after 1 number
Answer: 0.06
*If you end up with a number that has spaces after you stop fill with zeros
4|P age
Lesson – Estimation and Standard Form
Make your own notes section! (group examples)
• 49382 to 2 s.f.
Now you can try these
• 374.582 to 3 s.f. =
• 0.0009317 to 2 s.f. =
• 2.23 to 1 d.p =
• 3.56 to 2 s.f =
• 4.09 to 1 d.p =
• 3.349 to 2 s.f =
• 2.9239 to 3 d.p =
• 468779 to 3 s.f =
• 13013 to 1 s.f =
• 41.577 to 2 d.p =
5|P age
Lesson – Estimation and Standard Form
Standard Form
Standard Form is sometimes called scientific notation and is a way of representing very large
(or very small) numbers without them becoming visual puzzles which can fool the eye.
Common uses of it in science include representing the speed of light and the distance
between planets.
Example
• If we take the number 3 000 000 000 000
• It won’t fit on most calculators as it is too big! We need a way to represent this.
• We could say it is 3 with 12 zeros or
• 3 x 1,000,000,000,000
• We can write 1,000,000,000,000 as 1012
• We can say that:
3,000,000,000,000 is 3 x 1012
• What we can see is that the format is
(number between 1 and 10) x 10(some number)
Write your own notes
a) Write 500 in standard form
6|P age
Lesson – Estimation and Standard Form
Now try thsee
a) 4000
b) 60,000
c) 900,000
d) 7000,000
However, It is not always this easy.
Example
• Write 39,000 in standard form
Based on the previous examples we would say that is:
39 x 103
But this number
must be between 1
and 10!
So we put the first number as 3.9 which means we are going to have to multiply by 10 more!
3.9 x 104
The rule I use is that I cover up the first number and count how many digits come after. This
is my power.
OR
7|P age
Lesson – Estimation and Standard Form
Make your own notes
• Convert 146,300 to Standard Index Form
Can we convert to a whole number if we are given the number in standard form?
Of course we can.
Example
• Write 4.2 x 103 in normal decimal notation
o This is 4.2 x 1000
o 42 x 1000 = 42 000
o 1 number after a decimal point so
o 4.2 x 103 = 4200.0 or 4200
OR
8|P age
Lesson – Estimation and Standard Form
Now you can try these:
• 9.432 x 105 in normal decimal notation
• 4.1 x 103 in normal decimal notation
• 1.559 x 106 in normal decimal notation
Very Small Numbers
Example
• Write 0.0005 in standard form
We know the first number must be between 1 and 10 so we can see that number will be
5.
One simple rule for this calculation
• Count how many zeroes you see and that is the negative power
We can see 4 zeroes
So:
0.0005 = 5 x 10-4
9|P age
Lesson – Estimation and Standard Form
Now you can try these:
• Write 0.00183 in standard form
• Write 9.4 x 10-4 in decimal notation
• Write 2.73 x 10-2 in decimal notation
• Write 3 x 105 in decimal notation
• Write 6.4 x 103 in decimal notation
• Write 2.81 x 106 in decimal notation
• Write 6 x 10-2 in decimal notation
• Write 5.9 x 10-4 in decimal notation
• Write 3.783 x 10-7 in decimal notation
• Write 560000 in standard form
• Write 3040 in standard form
• Write 391000000 in standard form
• Write 0.007 in standard form
• Write 0.0000064 in standard form
• Write 0.21 in standard form
10 | P a g e
Lesson – Estimation and Standard Form
Calculating using Standard Form
These come up on the calculator paper questions
Your calculator will have 2 possible buttons that can be used to help with standard form
Exp
x
x 10
Find which one your calculator has!
• To enter 6.2 x 103
• Type 6 . 2
Exp 3 (substitute Exp for x10x as appropriate)
• To enter 9.483 x 10-6
• Type 9 . 4 8 3
Exp - 6
Example
• Calculate 2 x103 x 3 x 105
*Without using a calculator you will be able to do this once you know the rules of indices!
• Answer : 6 x 108
11 | P a g e
Lesson – Estimation and Standard Form
Now these yourself
• 8 x 104 ÷ 2 x 102
• 2.45 x 103 x 1.6 x 105
• 4.5 x 10-6 ÷ 3 x 10-2
• 3.4 x 102 + 4.18 x 104
• 2.11 x 105 - 9.6 x 103
• 4 x 10-2 + 6.3 x 10-1
• 5.7 x 105 - 2.6 x 10-3
Write down everything you remember from today’s session in the brain below!
12 | P a g e
Lesson – Estimation and Standard Form
13 | P a g e
Lesson – Estimation and Standard Form
Write the following as
decimal (normal)
numbers:
a) 4.74 x 108
b) 1.9 x 102
c) 8.62 x 106
d) 6.4 x 104
e) 3.5 x 104
f) 6.63 x 107
g) 9.09 x 108
Calculate the following:
h)
6 x 103 x 8.71 x 109
i) 1.36 x 10-10 - 9.5 x 10-10
j) 6.38 x 10-5 ÷ 7.96 x 10-8
k) 5.6 x 10-6÷ 5.43 x 10-1
l)
4.8 x 10-3 + 1.61 x 10-4
Write the following
numbers in standard form:
a) 8300
b) 440000
c) 98700000
d) 0.000034
e) 0.00009301
f) 0.00043
14 | P a g e
Lesson – Estimation and Standard Form