 # Standard form subtraction

To subtract 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

Calculate the following giving your answer in standard form

6.2times10^-5-5.06times10^-7

## Method 1

Actually carry out the subtraction

6.2times10^-5-5.06times10^-7

is the same as:

6.2/(10times10times10times10times10)-5.06/(10times10times10times10times10times10times10)

Which is

0.000062-0.000000506

which is

 0.000062000 - 0.000000506 0.000061494

remember move decimal place to right and -1 to the power.

or 6.1494times10^-5

## Method 2

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

6.2times10^-5-5.06times10^-7

Make the power of 10 the same

So this calculation is the same as

remember move the decimal place to the right and -1 to the power

is the same as 620times10^-7-5.06times10^-7

which is (620-5.06)times10^-7

614.94times10^-7

Now put this in standard form

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

6.1494times10^-5

Example 2

(8.73times10^8)-(2.18times10^5)

## Method 1

Actually carry out the subtraction

(8.73times10^8)-(2.18times10^5)

is the same as

8.73times10times10times10times10times10times10times10times10-2.18times10times10times10times10times10

which is

873,000,000-218,000

which is

 1 1 1 = 8 7 3, 0 0 0, 0 0 0 1 3 2 - cancel2 cancel1 8, 0 0 0 8 7 2, 7 8 2, 0 0 0

But in standard form this is

8.72782times10^8

## Method 2

An alternative way is to subtract indices but you need to make the powers of 10 the same.

8.73times10^8-2.18times10^5

is the same as

8.73times10^8-0.00218times10^8

Now because the powers are the same we can subtract

8.73times10^8-0.00218times10^8

is (8.73-0.00218)times10^8

(8.72782)times10^8

=8.72782times10^8

Which is already in standard form.

Example 3

(3.62times10^-8)-(6.14times10^-10)

## Method 1

Actually carry out the subtraction

(3.62times10^-8)-(6.14times10^-10)

is the same as

3.62/(10times10times10times10times10times10times10times10)

-6.14/(10times10times10times10times10times10times10times10times10times10)

which is

0.000,000,036,2-0.000,000,000,614

which is

 1 1 1 = 0. 0 0 0, 0 0 0, 0 3 6, 2 0 0 1 7 2 - 0. 0 0 0, 0 0 0, 0 0 cancel0, cancel6 cancel1 4 0. 0 0 0, 0 0 0, 0 3 5, 5 8 6

Now put in standard form

remember move decimal to the right and -1 to the power

3.5586times10^-8

## Method 2

(3.62times10^-8)-(6.14times10^-10)

Subtract using indices but first make the power of 10 the same

remember move the decimal place to the right and -1 to the power

So 362times10^-10=3.2times10^-8

therefore the calculation becomes

362times10^-10-6.14times10^-10

(362-6.14)times 10^-10

=355.86times10^-10

Now put in standard form

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

3.5586times10^-8