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Hi, I'm M.

Davies.

In this lesson, we're going to be adding two numbers that are written in standard form.

When adding numbers in standard form, we're going to convert them into ordinary numbers.

3 times 10 to the power of 4 is 30,000.

5 times 10 to the power of 4 is 50,000.

If we add these together, it gives us 80,000.

We then need to convert this back into standard form.

This is 8 times 10 to the power of 4.

In our next example, our powers are negative.

This means when we convert these numbers into ordinary numbers, they're going to be decimals.

5.

7 times 10 to the power of -3 is 0.

0057.

3.

1 times 10 from the power of -3, it's ordinary number is 0.

0031.

These are added to make 0.

0088.

When we convert this back into standard form, we get 8.

8 times 10 to the power of -3.

You might have noticed that the final answers on both of these examples are simply the two numbers that are in standard form times by 10 to the power 4 in the first example, and 10 to the power of -3, in the second example.

This only works when the powers are the same.

Our next example is this.

Again, we're going to convert these numbers into ordinary numbers.

This gives us 38,000 add 74,000 which is equal to 112,000.

In standard form, this is 1.

12 times 10 to the power of 5.

If we added 3.

8 and 7.

4, this is 11.

2.

If we were to write 11.

2 times 10 to the power of 4, this is an incorrect standard form.

Our final example is this one.

We're going to convert them into ordinary numbers and then add them together.

This gets 0.

0116.

And then convert this into standard form.

1.

16 times 10 to the power of -2.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

In question two, you needed to adjust your answer to make sure it was written in the correct standard form.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

Michael hasn't lined up the numbers correctly according to their place value when he's added them together.

The correct answer is 3.

75 multiplied by 10 to to the power of 4.

In this example, the powers aren't the same, so we definitely need to convert them into ordinary numbers first.

If we convert these into ordinary numbers, we get 300,000 add 50,000, this gives us 350,000.

We can then convert that into standard form, which is 3.

5 times 10 to the power of 5.

In our second example, our powers aren't the same again, but this time they are negative.

Meaning, we're going to be working with decimals.

We convert these numbers into ordinary numbers, we get 0.

00038 add 0.

0074.

When adding these together, make sure that your numbers are lined up correctly by their place value.

When we add these together, it gives us 0.

00778.

If we convert that into standard form, we get 7.

78 times 10 to the power of -3.

Here are some questions for you to try.

Pause the video to complete your task, and resume once you're finished.

Here are the answers.

You need to convert the standard form to ordinary numbers before adding them.

Just remember to convert them back into proper standard form.

Here is a question for you to try.

Pause the video to complete your task, and resume once you're finished.

Here is the answer.

England's population is approximately 56 million.

Scotland's population is approximately 5,400,000.

Wales' population is approximately 3,100,000.

The total, including Northern Ireland, is approximately 66,380,000.

If we write this in standard form, it is 6.

638 multiplied by 10 to the power of 7.

That's all for this lesson.

Thanks for watching.