Scientific notation is used to express very large or small numbers. It involves moving the decimal point in a number to the right or left by a power of 10. Positive powers of 10 move the decimal point right to express large numbers, like distances between planets. Negative powers of 10 move the decimal point left to express small decimal numbers, like distances between atoms. To convert a number to scientific notation, the decimal is moved to create a number between 1 and 10, and the power of 10 indicates how many places the decimal was moved.

1. Scientific Notation
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Powers of 10 Exponents, (called Scientific Notation), are used to
specify very large amounts, such as the distance between stars
and Planets. Earth to Moon Distance is about 4 x 105
km.

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Negative Powers of 10 Exponents, (called Scientific Notation), are
used to specify very small decimal amounts, such as the distance
between Silicon atoms in a Silicon Crystal which is 2.35 x 10-10
m.

4. 1.496 x 108
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149 600 000 km
Power of 10 MagnitudeNumber between
1 and 10 X

5. Keep in mind at all times the following:
1.496 x 108
= 149 600 000
Normal Numbers bigger than 1, or large numbers,
always have a POSITIVE Power of 10.
Values smaller than 1, usually decimal values,
always have a NEGATIVE Power of 10.
6.2 x 101
= 62
6.234 x 10-1
= 0.6234
2.31 x 10-3
= 0.00231

6. Move the Decimal Point eight to the Right
Move the Decimal Point three to the Left.
2.31 x 10-3
= 0.00231
1.496 x 108
= 149 600 000
The Power of 10 value gives us key information
about how many places to move the
Decimal Point to make Number values.

7. 1.5  104
Scientific Notation involves moving decimals.
1.5 0 0 0
Because the exponent is Positive
4, move the decimal point 4 places
to the right.
Add in Zeroes to fill the empty gaps.
5.8  10-4
0 0 0 0 5.8
Because the exponent is a Negative
4, move the decimal point 4 places
to the left.
Add in Zeroes to fill the empty gaps.0.00058
15 000
=
=
=
=

8. 2.756  105
Scientific Notation involves moving decimals.
2.7 5 6 0 0
Because the exponent is Positive
5, move the decimal point 5 places
to the right.
Add in Zeroes to fill the empty gaps.
3.76  10-3
0 0 0 3.76
Because the exponent is a Negative
3, move the decimal point 3 places
to the left.
Add in Zeroes to fill the empty gaps.0.00376
275 600
=
=
=
=

9. 7.74521  105
Scientific Notation involves moving decimals.
7.7 4 5 2 1
Because the exponent is Positive
5, move the decimal point 5 places
to the right.
No Zeroes needed to fill empty gaps.
6  10-3
0 0 0 6.
Because the exponent is a Negative
3, move the decimal point 3 places
to the left.
Add in Zeroes to fill the empty gaps.0.006
774 521
=
=
=
=

10. 1.5  104
1 5 0 0 0
The Number is Greater than 10,
so the Exponent will be Positive.15 000
=
Move the Decimal point to the LEFT
to create a number between 1 and 10.
Remove Zeroes that are not needed.1.5 0 0 0=
We moved 4 places so
Power of 10 is four : 104=
4 places

11. Does 1.5  104 15 000 ?=
1.5  104
1.5 0 0 0
Because the exponent is Positive
4, move the decimal point 4 places
to the right.
Add in Zeroes to fill the empty gaps.15 000
=
=
It is a Good Idea to check all Scientific Notation
Answers by working backwards from the answer
to the Original given value we had at the start.
Originally we started off with 15 000, so we are right!
Our Answer to Question Original Starting Value

12. 4.3  10-3
0 .0 0 4 3
The Number is a decimal less than 1,
so the Exponent will be Negative.0.0043
=
Move the Decimal point to the RIGHT
to create a number between 1 and 10.
Remove Zeroes that are not needed.0 0 0 4.3=
We moved 3 places so
Power of 10 is three : 10-3=
3 places

13. 5.0  10-3
0 .0 0 5 0
The Number is a decimal less than 1,
so the Exponent will be Negative.0.0050
= Move the Decimal point to the RIGHT
to create a number between 1 and 10.
Remove Zeroes that are not needed.
NEVER REMOVE ZEROES THAT
CAME AFTER A DECIMAL POINT.
0 0 0 5.0=
We moved 3 places so
Power of 10 is three : 10-3
=
3 places

14. 1  103 or 103
1 0 0 0
The Number is Greater than 10,
so the Exponent will be Positive.1000
=
Move the Decimal point to the LEFT
to create a number between 1 and 10.
Remove Zeroes that are not needed.1.0 0 0=
We moved 3 places so
Power of 10 is three : 103=
3 places

15. 8  100
8
The Number is NOT Greater than 10,
so the Exponent will NOT be Positive.8
=
8 is already a number between 1 and 10.
so we move the decimal ZERO places.
There are no Zeroes that need removal.8=
We moved 0 places so
Power of 10 is zero : 100=

16. Express 3.45 x 106 as a number value.
On the calculator, scientific notation is
done with the or button.
3.45 x 106 is typed as 3.45 6
and appears as 3.45*10^6 or 3.45E6
x10n
x10n
Pressing “enter” gives : 3 450 000

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