Whole Numbers
Numbers · Whole Numbers
CBC Grade 5 Mathematics — Whole Numbers
Lesson Objectives
By the end of this topic, a learner should be able to:
- Identify the place value and total value of digits in numbers up to hundreds of thousands
- Read and write numbers up to tens of thousands in words
- Order numbers up to tens of thousands
- Round off numbers to the nearest hundred and thousand
- Apply divisibility tests for 2, 5, and 10
- Determine the HCF and LCM of given numbers
- Appreciate the use of whole numbers in real-life situations
Whole Numbers
Whole numbers are the numbers we count with, together with zero. In Grade 5 we go up to hundreds of thousands.
a) Place value and total value
Every digit has a place. From the right the places are ones, tens, hundreds, thousands, ten thousands, hundred thousands.
The place value is what that position is worth.
The total value is the digit multiplied by its place value.
Write big numbers in groups of three from the right. It makes them much easier to read.
b) Reading and writing
Read the thousands group first, then say "thousand", then read the rest.
So 34 250 is thirty-four thousand, two hundred and fifty.
c) Ordering numbers
Count the digits first. More digits means a bigger number.
If they have the same number of digits, compare from the left. The first place where they differ decides it.
d) Rounding
To round to the nearest hundred, look at the tens digit. To round to the nearest thousand, look at the hundreds digit.
If that digit is 5 or more, round up. If it is less than 5, round down.
Everything after becomes zero.
Take 4 738 to the nearest hundred. The tens digit is 3, so it becomes 4 700.
e) Divisibility tests
These tell you if a number divides exactly, without doing the division.
| Divides by | Test |
|---|---|
| 2 | the last digit is even |
| 5 | it ends in 0 or 5 |
| 10 | it ends in 0 |
So 470 divides by 2, by 5 and by 10. But 472 divides by 2 only.
f) HCF and LCM
A factor divides into a number exactly. The HCF is the biggest factor two numbers share.
A multiple is what you get in the times table. The LCM is the smallest multiple both numbers share.
HCF is small, LCM is large. If your HCF is bigger than both numbers, something is wrong.
g) Where this is used
Counting money. Reading the population of a town. Sharing things into equal groups. Working out when two things happen together.
:::checkpoint Check yourself
- What is the total value of the 6 in 264 300?
- Round 5 482 to the nearest hundred.
- Does 385 divide by 5? How do you know?
- Find the HCF of 8 and 12. :::
Definitions
- Place value — the value of a digit based on its position.
- Total value — a digit multiplied by its place value.
- Factor — a number that divides exactly into another.
- Multiple — the result of multiplying a number by a whole number.
- HCF — the largest number that divides exactly into two or more numbers.
- LCM — the smallest number that two or more numbers divide into exactly.
Must Remember
- When rounding, look only at the digit immediately to the right of the place you're rounding to.
- A number ending in 0 is divisible by 2, 5, and 10 all at once.
- HCF is the highest shared factor — list all common factors before picking the highest.
- LCM is the lowest shared multiple — don't assume it's just the two numbers multiplied together.
- When writing numbers in words, "and" goes between hundreds and tens/ones.
Conclusion
Every skill here comes down to understanding what a number is made of. Check your own work by asking: does my rounded answer make sense next to the original number? Do my listed factors actually divide in evenly?