Standard form addition
To add in standard form all you need to remember is
Make the powers of 10 the same
NOTE:
To make the power of 10 the same remember
0.001
is the same as 0.01×10-1 (Move decimal right and -1 to the power)
is the same as 0.1×10-2 (Move decimal right again and -1 to the power again)
is the same as 1.0×10-3 (Standard form)
is the same as 0.0001×101 (Move decimal left and +1 to the power)
is the same as 0.00001×102 (Move decimal left again and +1 to the power again)
Example 1
Work out the following giving your answer in standard form
3.8×104+8.24×105
Method 1
Actually carry out the addition
3.8×104+8.24×105
is the same as
| 3.8×10×10×10×10 | + | 8.24×10×10×10×10×10 |
| 38,000 | + | 824,000 |
Which is
| 824,000 | |
| + | 38,000̲ |
| 862,000 |
Convert to standard form
remember move decimal place to the left and +1 to the power.
Which is 8.62×105
Method 2
An alternative way is to add the indices but you need to make the powers the same
3.8×104+8.24×105
and making the powers of 10 the same
0.38×105+8.24×105
Which is
(0.38+8.24)105
and this equals
8.62×105 (already in standard form)
Example 2
Work out the following giving your answer in standard form
8.04×10-6+7.63×10-7
Method 1
Is to actually carry out the calculation
8.04×10-6+7.63×10-7
| = | 8.0410×10×10×10×10×10 | + | 7.6310×10×10×10×10×10×10 |
| = | 0.00000804 | + | 0.000000763 |
| = | 0.000008040 | ||||||||
| + | 0.000000763 | ||||||||
| 0.000008803 | |||||||||
| 1 | |||||||||
| = | 0.000008803 |
remember move decimal place right and -1 to the power.
But in standard form =8.803×10-6
Method 2
An alternative way is to add the indices but you need to make the powers the same.
8.04×10-6+7.63×10-7
Would become
80.4×10-7+7.63×10-7
(80.4+7.63)×10-7
Which equals
(88.03)×10-7
which is
88.03×10-7
But we need this in standard form
and remember move decimal place to the left and +1 to the power.
is the same as 8.803×10-6
Answer: is 8.803×10-6
Example 3
Work out the following giving your answer in standard form
(8×100)+(4.6×10-3)
Method 1
Is to actually carry out an addition calculation
NOTE:
any power to zero =1
| (8×100) | + | (4.6×10-3) |
| (8×1) | + | (4.6×10-3) |
| 8 | + | 0.0046 |
| = | 8.0000 | |
| + | 0.0046̲ | |
| 8.0046 |
=8.0046
and this is already in standard form
Method 2
Is actually add up the indices or powers but only if they are the same power.
So change
(8×100)+(4.6×10-3)
is
(8000×10-3)+(4.6×10-3)
which is
(8000+4.6)×10-3
=8004.6×10-3
But we need this in standard form
remember move decimal place to left and +1 to the power.
So 8004.6×10-3
Becomes 8.0046
Answer: 8.0046
