Chapter 1. Whole Numbers: Counting, Ordering and Place Value FREE
Counting in Different Steps
In Grade 5 you will work with much bigger numbers than before, up to six digits, which means numbers as large as 999 999. You already know how to count forwards and backwards in ones. Now you will practise counting in steps of 2s, 3s, 5s, 10s, 25s, 50s and even 100s. For example, counting in 25s is very useful because 25 cents make up a quarter of a rand, so you might count 25, 50, 75, 100 when working with coins. Counting backwards is just as important as counting forwards, because it helps you understand how numbers decrease and prepares you for subtraction.
Comparing and Ordering Numbers
When you have two or more numbers, you often need to know which one is bigger or smaller. We use special symbols for this: < means "is less than", > means "is greater than", and = means "is equal to". For example, 45 231 < 45 321 because when we compare digit by digit from the left, the ten-thousands and thousands are close, but the hundreds digit makes the second number bigger. Learning to order numbers from smallest to biggest, or biggest to smallest, is a skill you will use often, such as when comparing the population of different South African towns or the distances between cities like Cape Town and Durban.
Place Value
Every digit in a number has a value depending on its position. In a 6-digit number, the positions from right to left are units, tens, hundreds, thousands, ten-thousands and hundred-thousands. Take the number 384 725: the 3 is worth 300 000, the 8 is worth 80 000, the 4 is worth 4 000, the 7 is worth 700, the 2 is worth 20, and the 5 is worth 5 units. Writing a number this way, showing what each digit is really worth, is called expanded notation: 384 725 = 300 000 + 80 000 + 4 000 + 700 + 20 + 5. Place value helps you read and work with large numbers correctly, such as the number of learners in all the schools in Gauteng.
Rounding Off Numbers
Sometimes we do not need an exact number, just a good estimate. Rounding off makes numbers simpler to work with. To round to the nearest 10, look at the units digit: if it is 5 or more, round up; if it is less than 5, round down. The same idea applies to rounding to the nearest 100 or 1 000, using the tens digit or the hundreds digit instead. For example, 3 847 rounded to the nearest 10 is 3 850, rounded to the nearest 100 is 3 800, and rounded to the nearest 1 000 is 4 000. Rounding is handy in everyday life, such as when a shopkeeper in Polokwane wants to quickly estimate the cost of a trolley of groceries.
- Count in intervals of 2, 3, 5, 10, 25, 50 and 100, forwards and backwards
- Use <, > and = to compare and order numbers up to six digits
- Identify the place value of each digit and write numbers in expanded notation
- Round numbers off to the nearest 10, 100 and 1 000