Scientific Notation
Handling very big and very small numbers
Why we need it
Scientific notation is just
a way of writing
very large
or
very small
numbers without having
to use a bazillion zeros.
The Powers of 10
NOTICE
Multiplying by a power of 10 puts zero(s)
on the end of the number
2 x 10 = 20
Multiplying by 100 (102) puts on 2 zeros
2 x 100 = 200
Multiplying by 1000 (103) puts on 3 zeros
2 x 1000 = 2000
etc.
How can we use this?
Let’s use this feature of multiplying by
powers of 10 to write 2 billion without a
bunch of zeros.
2,000,000,000
To get that we must have multiplied
2 x 1,000,000,000
or 2 x 109
Rolling the Decimal
Or you can think of it as “rolling the decimal”
2. x 10 = 2.0. rolls 1 place
Multiplying by 100 (102) puts on 2 zeros
2. x 100 = 2.00. rolls 2 places
Multiplying by 1000 (103) puts on 3 zeros
2. x 1000 = 2.000. rolls 3 places
etc.
Let’s Make a Rule!
If we have a BIG number like
2,300,000
let’s write the non-zero part as a decimal
with just one digit to the left of the point
2.3
and account for all the other places as a
power of 10
Let’s Make a Rule!
To get the decimal from where it started
2,300,000.
To where it is now, between the 2 and 3
2.300,000.
it had to move 6 places to the left.
2.3 x 106
Let’s Go the Other Way!
What if we start with a very small
number and have to roll the decimal the
other way?
To indicate that we started with a small
number, we’ll use a negative exponent
on the 10.
Let’s Go the Other Way!
Let’s write .0000789 in scientific notation
.0000789
Roll that decimal!
.00007.89
It moved 5 places to the right.
7.89 x 10-5
Right or Left?
I can never keep straight which way to go!
An Easy Way to Remember!
Put one digit to the left of the point.
If it’s a BIG number, the exponent is +
If it’s a little number, the exponent is -
2,340,000,000 = 2.34 x 109
.0000000234 = 2.34 x 10-8