Chapter 1. Getting Started: Whole Numbers up to 9-digit Numbers FREE
1. Getting Started: Whole Numbers up to 9-digit Numbers
Welcome to Grade 6 Mathematics! This year you will work with much bigger numbers than before. By the end of this chapter you will be able to read, write, order and round whole numbers all the way up to 9-digit numbers (that is hundreds of millions). These are the kinds of numbers we use to count people in a country, money in a big business, or kilometres in space.
Place value up to hundreds of millions
Every digit in a number has a place value that tells us how much it is worth. As we move to the left, each place is 10 times bigger than the one before it. The places, from right to left, are:
- Units (ones)
- Tens
- Hundreds
- Thousands
- Ten-thousands
- Hundred-thousands
- Millions
- Ten-millions
- Hundred-millions
To make big numbers easy to read, we leave a space between every group of three digits, starting from the right. For example, we write 462 815 309, not 462815309.
Reading a 9-digit number
Take the number 462 815 309. We read it in groups: four hundred and sixty-two million, eight hundred and fifteen thousand, three hundred and nine. The space helps you see the millions group, the thousands group, and the units group.
Expanded notation
Expanded notation means writing a number as the sum of the value of each digit. Look at 3 027 540:
\(3\,027\,540 = 3\,000\,000 + 0 + 20\,000 + 7\,000 + 500 + 40 + 0\)
Notice that the zeros are place-holders. The 0 in the hundred-thousands place keeps the other digits in their correct positions, even though it adds nothing to the total.
Comparing and ordering numbers
To compare two whole numbers, first count how many digits each one has. The number with more digits is bigger. If they have the same number of digits, compare from the left, digit by digit, until the digits differ.
We use these symbols:
- (>) means "is greater than"
- (<) means "is less than"
- (=) means "is equal to"
Worked example: Compare 5 280 000 and 5 280 900.
Both have 7 digits. Reading from the left, the millions, hundred-thousands, ten-thousands and thousands match. The difference is in the hundreds: 0 versus 9. So \(5\,280\,000 < 5\,280\,900\).
To put numbers in ascending order means smallest to biggest; descending order means biggest to smallest.
Rounding off whole numbers
Rounding helps us estimate. To round a number, look at the digit just to the right of the place you are rounding to:
- If that digit is 5 or more, round up.
- If it is 4 or less, round down (keep the same).
Example 1 (nearest 10): Round 3 478 to the nearest 10. The units digit is 8, which is 5 or more, so we round up to 3 480.
Example 2 (nearest 100): Round 3 478 to the nearest 100. The tens digit is 7, so we round up to 3 500.
Example 3 (nearest 1 000): Round 3 478 to the nearest 1 000. The hundreds digit is 4, which is 4 or less, so we round down to 3 000.
Why this matters in real life
Imagine the city of Johannesburg has about 5 635 127 people. A newspaper might round this to 5 600 000 (about 5,6 million) so it is easier to talk about. If you buy a car for R249 999, the salesperson might say it costs "about R250 000". Rounding gives us a quick, sensible picture without all the small detail.
Quick summary
- Each place is 10 times the place to its right.
- Group digits in threes with a space: 462 815 309.
- Use expanded notation to show the value of every digit.
- Compare by number of digits first, then from the left.
- Round by looking at the next digit: 5 or more rounds up.
Well done! These skills are the foundation for adding, subtracting, multiplying and dividing the big numbers you will meet in the next chapters.