﻿Hi, I'm Mr Chan, and in this lesson, we're going to learn how to convert large numbers to standard form. Standard form is a way of writing very large number or very small numbers, and they all must fit this format where we have a number that's between 1 and 10, so the first part must be greater than 1 and it also must be less than 10, and it's multiplied by a power of 10. The power of 10 we call an index number, and that index number must be a positive or negative whole number. Let's have a look at some examples. The first example 2 times 10 to the power of 3. So the first part is greater than 1, and also less than 10. The power of 10 being 3, that fits the bill quite well, so that's a standard form number. The second example 4.6, which is greater than 1 and less than 10, multiplied by 10 to the power of 21. Again, that is a positive whole number, that's the index number, so that's a great example of another standard form number. The third example 5.01 times 10 to the power of negative 12. The first part of the standard form number is fine, 10 to the power of negative 12 is also fine, the index number is allowed to be negative, and it's a whole number. Here's some examples that aren't standard form numbers. 0.3 times 10 to the power of 3. The problem with that, is the first part, 0.3 is less than one. Remember, it must be greater than 1 for it to be a standard form number. The next example, 15.6 times 10 to the power 12. We can see the first part of the standard form number 15.6 is greater than 10, so that's not a standard form number. The third example, 6.04 times 10 to the power 0.5. We can see the index number here, 0.5, it's not a whole number, so that's again, not a standard form number. So let's recap some powers of 10. We're starting with 10 to the power of 2, 10 squared. The index number 2 tells us that the 10 is being repeatedly multiplied by itself twice, so 10 times 10 equals 100. 10 to the power of 3, 10 times 10 times 10, that equals 1,000. 10 to the power of 4, that tells us it's 10 repeatedly multiplied by itself 4 times, 10 times 10 times 10 times 10, that equals 10,000. Let's have a look at multiplying by powers of 10, things that we've learned in the past. So we have the question, 1.34 times 10. Now when we multiply by 10, we shift the numbers one space to the left as so. To get an answer, 13.4. The next example, we're multiplying 5.4 by 1,000. So what we do when we're multiplying by 1,000 is shift the numbers three spaces to the left of the decimal point. You notice that we shift the number of places according to how many zeros that we've got in the power of 10. So in this case, multiply by 1,000, 1,000 has got three zeros, we shift 5.4 three spaces, we get an answer 5,400, and notice also we've put some zeros in where there would be empty spaces in the place value. Here are some questions for you to try. Pause the video to complete the task, and restart the video when you're finished. Here are the answers. Hopefully you've seen the link in question one between how many zeros there are, and the index number in the power of 10. Here are some more questions for you to try. Pause the video to complete the task, and restart the video when you're finished. Here are the answers. In part A, we're thinking of 6,000 as 6 times 1,000, to give a standard form answer, 6 times 10 to the power of 3. In part B, one million is 1 times 10 to the power of 6. And in part C, 3200 we can rewrite as 3.2 times 1,000. We know 1,000 is 10 to the power of 3, so as a standard form answer, 3.2 times 10 to the power of 3. Hopefully you got the others correct as well. Let's begin converting large number to standard form. Here's my first example, 800. I'm going to think of 800 as 8 times 100. Because I know a standard form number must begin with a number greater than one, but less than 10. The multiplied by 100, I'm going to think of that now as 10 squared. So what we can do now is write 800 as a standard form number 8 times 10 squared. Here's another example, 45,000. The way I'm going to think about writing 45,000 as a standard form number, is 4.5 times 10,000. And I'm going to think of the 10,000 as 10 to the power of 4. So rewriting 45,000 as a standard form number gives us 4.5 times 10 to the power of 4. Here are some questions for you to try. Pause the video to complete the task, resume the video once you're finished. Here are the answers. Let's look at question five. The distance from the Earth to the Moon is 384 million metres. Wow, that is a very big number. So we've got to write that number in standard form. So how we think about that number is 3.84 multiplied by 100 million. So when we think about that as standard form, we would write the number 3.84 multiplied by 10 to the power of 8. Here are some questions for you to try. Pause the video to complete the task, restart the video when you're finished. Here are the answers. In question seven, we're told that Mount Everest is 8,800 metres high. We have to convert this number into centimetres. We do know that in 1 metre, there are 100 centimetres, so we're going to have to multiply that 8,800 by 100, to give an answer in centimetres 880,000cm. In part B, writing that large number down in standard form, we get an answer 8.8 times 10 to the power of 5. That's all for this lesson. Thanks for watching.

In this lesson, we will convert large ordinary numbers to a standard form number with positive powers of ten.

Maths

Y10 Maths (Core)

Key Stage 4

Year 10

Convert large numbers to standard form

Y11 Maths (Foundation)

Year 11

Standard Form (Writing and converting)

Number (N)

THEME

UNIT

Convert large standard form numbers to ordinary form

Convert small numbers to standard form

Convert small standard form numbers to ordinary form

Work out the missing index number for the calculation 2.650 x 10ⁿ = 2650

Write one million in standard form.

Write 280,000 in standard form.

Why is 78.12 x 10⁵ not a standard form number?

Write 5.81 x 10⁶  in ordinary form.

Which number is smaller? 3 x 10⁴ or 4 x 10³

Which power of ten is equivalent to 0.01?

Complete the missing number in this calculation 5 ÷ ? = 0.05

Write 0.0003 in standard form.

Which number is smaller? 3 x 10⁻⁴ or 4 x 10⁻³

Write 4 x 10⁻³ in ordinary form.

Write 2.05 x 10⁻⁶ in ordinary form.

Which number is smaller? 5 x 10⁻⁴ or 4 x 10⁻⁵

Lesson overview:Convert large numbers to standard form

Core Content

Pupils Will Learn

Standard Form (Writing and converting):