Combining numbers in scientific notation:Numbers expressed in scientific notation have a number multiplied by a power of ten.
When multiplied or divided, the number parts and power of ten parts are combined separately to give the result in scientific notation.
| A small number
2.5 × 10–5 | A large number
3.2 × 109 |
|
2.5 × 10–5 × 3.2 × 109 =
(2.5 × 3.2) × (10–5 × 109) =
8.0 × 104 |
To add or subtract numbers in scientific notation, the
exponents on the powers of ten must be the
same.
If they are not the same,
one exponent on a power of 10 must be adjusted
by multiplying by a power of ten.
Then divide pre-exponential term by the same power of ten.
Adding 1.03 × 10–4 to 3.56 × 10–3 requires adjusting one power of ten.
It is better to adjust the power of 10 in the smaller of the two numbers.
To adjust 1.03 × 10–4
Multiply the power of ten by 10 and divde the pre-exponential term by 10.
This gives give 0.103 × 10–3
Once the exponent in the power of 10 for the two numbers is the same, the number parts of the two can be added. The result has the same power of ten as the two numbers added.
The sum of the two numbers above is then equal 3.663 × 10–3
Your calculator does this all for you. Practice by entering the two numbers before the adjustment and make sure that you get the sum given.