This Year 6 place value to 10 000 000 and rounding lesson is written for pupils aged 10-11 and follows the National Curriculum. In short, it shows you how to work with numbers up to 10 million, negative numbers and rounding. Before you start, you can look back at Year 5 maths if you need a quick reminder.
Year 6 place value to 10 000 000 and rounding lesson: what you will learn
Numbers can be very large. In Year 6 you work with numbers up to 10 000 000, round them to any degree of accuracy and use negative numbers.
Starter activity
Lena reads in a newspaper: "About 9 000 000 people live in London." The exact number in the census was 8 866 540. why does the newspaper use a different number? In this chapter you will learn how to read, write, compare and round numbers as big as 10 000 000 so you can decide which degree of accuracy is sensible.
Reading and writing big numbers
Definition: place value
Place value tells us what each digit is worth. The columns, from the right, are ones, tens, hundreds, thousands, ten thousands, hundred thousands, millions and ten millions.Example 1
Write 6 305 207 in words.
Six million, three hundred and five thousand, two hundred and seven.
The value of a digit
Example 2
What is the value of the 3 in 6 305 207?
The 3 is in the hundred thousands column, so its value is 300 000.
Note
A zero holds a place. In 6 305 207 there are 0 ten thousands and 0 tens.
Comparing and ordering numbers
Rule: ordering numbers
A number with more digits is larger. If the number of digits is the same, compare the digits from the left. Use < and > to show which is smaller.
Example 3
Order 4 560 000, 4 506 000 and 4 650 000, smallest first.
All have seven digits and start with 4. Compare the next digits: 5, 5, 6. Then compare 4 560 000 with 4 506 000: the next digits are 6 and 0. The order is 4 506 000, 4 560 000, 4 650 000.
Counting on and back in powers of ten
Key fact: powers of ten
10, 100, 1 000, 10 000 and so on are powers of ten. Counting on 10 000 changes only the ten thousands digit.
Example 4
What is 100 000 less than 2 350 000?
The hundred thousands digit goes from 3 to 2. The answer is 2 250 000.
Rounding
Method: rounding to a given place
- Find the digit in the place you are rounding to.
- Look at the digit to its right.
- If it is 5 or more, round up. If it is 4 or less, round down.
- Replace the digits to the right with zeros.
Example 5
Round 3 748 962 to the nearest 10 000 and the nearest million.
The thousands digit is 8, so round up to 3 750 000. The hundred thousands digit is 7, so round up to 4 000 000.
Example 6
Round 849 999 to the nearest 1 000.
The hundreds digit is 9, so round up. 849 999 rounds to 850 000.
Watch out
A 9 rounded up carries over to the next column, so 899 500 rounds to 900 000 to the nearest 1 000.
Negative numbers
Definition: negative number
A negative number is less than 0. On a number line the bigger a negative number looks, the smaller its value is.
Rule: negative numbers in context
To find the difference between two temperatures, count the steps on a number line. Going up from −7 to 5 is 7 + 5 = 12.
Example 7
The temperature falls from 3°C to −6°C. By how much does it fall?
3 down to 0 is 3, then 0 down to −6 is 6. The fall is 3 + 6 = 9 degrees.
More about place value and rounding
Method: comparing two big numbers
- Count the digits. The number with more digits is bigger.
- If both have the same number of digits, write them in a place value table.
- Compare the digits from the left, one column at a time.
- Stop at the first column where the digits are different. The bigger digit gives the bigger number.
Example 8
Write 5 060 308 in expanded form and say which digit is in the ten thousands column.
5 060 308 = 5 000 000 + 60 000 + 300 + 8. There is a zero in the hundred thousands column, a 6 in the ten thousands column, a zero in the thousands column and a zero in the tens column. The digit in the ten thousands column is 6.
Example 9
A stadium holds 62 480 fans. Round this to the nearest 1 000 and to the nearest 10 000.
For the nearest 1 000, look at the hundreds digit, which is 4. Round down: 62 000. For the nearest 10 000, look at the thousands digit, which is 2. Round down: 60 000. The same number gives different answers because the degree of accuracy is different.
Example 10
The temperature at the top of a mountain is −8°C. At the bottom it is 5°C. What is the difference?
Draw a number line. From −8 up to 0 is 8 degrees. From 0 up to 5 is 5 degrees. The difference is 8 + 5 = 13 degrees.
Watch out: common mistakes
Do not stop rounding at the digit you are rounding to. You must look at the digit after it. Also remember that a number such as 7 000 040 needs zeros in the empty columns, otherwise it looks like 740. When you order negative numbers, −10 is smaller than −2 even though 10 is bigger than 2.
Why do we round?
We round when an exact number is not needed or when it is quicker to estimate. A newspaper may round the population of a town to the nearest 100 000. A builder may round the cost of materials to the nearest £10 to check an answer. In a test you can use rounding to check that your answer is sensible. If you add 3 482 719 and 517 281, your estimate of 3 500 000 + 500 000 = 4 000 000 tells you the exact answer must be close to four million.
Did you know?
The word "million" comes from an Italian word meaning "a big thousand". People first used the word about 700 years ago. Before that, nobody needed a single word for such a huge number. Today the population of the whole world is around eight thousand million, which is eight billion.
Otto’s tip
Draw a place value table and write each digit in its column. It never lets you down!
How to use this Year 6 place value to 10 000 000 and rounding lesson
First, read the key points so that you know where the Year 6 place value to 10 000 000 and rounding lesson is going. Then work through each definition and worked example, and cover the solution before you read it. After that, practise with the place value to 10 000 000 and rounding worksheet and check every question with the worksheet answers. When you feel ready, test yourself with the multiple choice questions or the quick quiz. Finally, sit the place value to 10 000 000 and rounding test and mark it with the test answers.
Also, the starters are a good warm-up, so you can keep the key facts fresh. Moreover, all the pages of this chapter work together, so you can move between them at any time. For example, many pupils read the lesson on Monday, practise on Wednesday and test themselves on Friday. In short, this Year 6 place value to 10 000 000 and rounding lesson gives you everything you need for the chapter.
Similar pages
WorksheetPlace value to 10 000 000 and rounding – Year 6 maths worksheet with answers to download as PDF
AnswersPlace value to 10 000 000 and rounding – Year 6 maths worksheet answers to download as PDF
Multiple choice questionsPlace value to 10 000 000 and rounding – Year 6 maths multiple choice questions to download as PDF
QuizPlace value to 10 000 000 and rounding – Year 6 maths quiz to download as PDF
TestPlace value to 10 000 000 and rounding – Year 6 maths test to download as PDF
Test answersPlace value to 10 000 000 and rounding – Year 6 maths test answers to download as PDF
StartersPlace value to 10 000 000 and rounding – Year 6 maths starters to download as PDFOther chapters in this level
LessonThe four operations, order of operations and long division – Year 6 maths lesson to download as PDF
LessonFractions: add, subtract, multiply and divide – Year 6 maths lesson to download as PDF
LessonDecimals and percentages – Year 6 maths lesson to download as PDF
LessonRatio, proportion and percentages – Year 6 maths lesson to download as PDF
LessonAlgebra: formulae, sequences and missing numbers – Year 6 maths lesson to download as PDF
LessonConverting units, area, perimeter and volume – Year 6 maths lesson to download as PDF
LessonAngles, circles and 3D shapes – Year 6 maths lesson to download as PDF
LessonFour-quadrant coordinates and transformations – Year 6 maths lesson to download as PDF