 # 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   0.01times10^-1      (Move decimal right and -1 to the power)

is the same as   0.1times10^-2        (Move decimal right again and -1 to the power again)

is the same as   1.0times10^-3        (Standard form)

is the same as   0.0001times10^1    (Move decimal left and +1 to the power)

is the same as   0.00001times10^2  (Move decimal left again and +1 to the power again)

Example 1

Work out the following giving your answer in standard form

3.8times10^4+8.24times10^5

## Method 1

Actually carry out the addition

3.8times10^4+8.24times10^5

is the same as

 3.8times10times10times10times10 + 8.24times10times10times10times10times10 38,000 + 824,000

Which is

 824,000 + ul(38,000) 862,000

Convert to standard form

remember move decimal place to the left and +1 to the power.

Which is 8.62times10^5

## Method 2

An alternative way is to add the indices but you need to make the powers the same

3.8times10^4+8.24times10^5

and making the powers of 10 the same

0.38times10^5+8.24times10^5

Which is

(0.38+8.24)10^5

and this equals

8.62times10^5  (already in standard form)

Example 2

Work out the following giving your answer in standard form

8.04times10^-6+7.63times10^-7

## Method 1

Is to actually carry out the calculation

8.04times10^-6+7.63times10^-7

 = 8.04/(10times10times10times10times10times10) + 7.63/(10times10times10times10times10times10times10) = 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 =8.803times10^-6

## Method 2

An alternative way is to add the indices but you need to make the powers the same.

8.04times10^-6+7.63times10^-7

Would become

80.4times10^-7+7.63times10^-7

(80.4+7.63)times10^-7

Which equals

(88.03)times10^-7

which is

88.03times10^-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 8.803times10^-6

Answer: is 8.803times10^-6

Example 3

Work out the following giving your answer in standard form

(8times10^0)+(4.6times10^-3)

## Method 1

Is to actually carry out an addition calculation

NOTE:

any power to zero =1

 (8times10^0) + (4.6times10^-3) (8times1) + (4.6times10^-3) 8 + 0.0046

 = 8.0000 + ul0.0046 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

(8times10^0)+(4.6times10^-3)

is

(8000times10^-3)+(4.6times10^-3)

which is

(8000+4.6)times10^-3

=8004.6times10^-3

But we need this in standard form

remember move decimal place to left and +1 to the power.

So 8004.6times10^-3

Becomes 8.0046

Answer: 8.0046