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[h] Year 6 Maths Number and Place Value Study flashcards
[q] Place Value of Numbers
You can tell the value of a number by looking at the position of its digits.
[a]
Example
Let’s look at a seven-digit number:
8 734 256
In this number:
Thousands
• There are 8 millions = 8 000 000
Tens
• There are 7 hundreds of thousands = 700 000
(700 thousand)
• There are 3 tens of thousands = 30 000
(30 thousand)
• There are 4 thousands = 4000
• There are 2 hundreds = 200
• There are 5 tens = 50
• There are 6 units = 6
In the number six thousand seven hundred and four, you
will see that there are no tens.
6 7 0 4
You need to put a zero in the tens column as a place
holder to make sure all the other digits stay in their
correct positions.
[q] Ordering Numbers
You need to look at numbers to compare them and find out which number is greater.
[a]
Example
Which is greater? 3715 or 3742
Both numbers have 3 thousands and 7 hundreds so we
need to look at the next column – the tens column – to
compare them.
This means 3742 is greater than 3715.
You can write ‘greater than’ and ‘less than’ using symbols:
> means ‘is greater than’
< means ‘is less than’
So 3742 > 3715
[q] What are Negative Numbers?
Numbers below zero are called negative numbers. They have a ‘minus’ sign in front of them to show that they are negative numbers, for example −14, −465.
If you look at a number line, you can see that negative numbers count from 0 in the opposite direction to positive numbers.
[a]
Example–4 –3 –2
5 is greater than 2.
[q] Counting Using Negative Numbers
You can count back from 10 in 2s by taking away 2 each time:
[a]
If you continue to count back in 2s, you can go beyond
zero into negative numbers.
[q] Counting Sequences
You can count on or back from any number in equal steps. This is called a sequence.
You need to be able to count on or back from any number in jumps of any size.
[a]
Example
Counting from 5 in steps of 4:
Count back in 100s from 953:
5, 9, 13, 17…
953, 853, 753…
Sometimes you are not given the steps.
Example
What are the next three terms or numbers in
this sequence?
4, 10, 16,
First you need to work out the jump between each
number in our sequence.
[q] Rounding Numbers
Rounding numbers makes them easier to work with and can help you to estimate answers to calculations.
[a]
Example
To round 32 to the nearest 10, you have a choice of
rounding to 30 or 40:
When you look at a number line, you can see that 32 is
nearer to 30 than 40. So you round 32 down to 30.
The key for rounding to the nearest 10 is the units. If the
units are less than 5, you round down. If the units are 5 or
above, you round up.
Example
Round 365 to the nearest 100.
The key for rounding to the nearest 100 is the tens
column. If the tens digit is less than 5, round down.
If the tens digit is 5 or above, round up.
To round to the nearest 1000, you need to look at the
hundreds column. If the hundreds digit is 5 or above,
round up. If the hundreds digit is below 5, round down.
Example
Round 4765 to the nearest 1000.
[q] Rounding to the Nearest 10 000
or 100 000
To round to the nearest 10 000, look at the thousands digit.
If it is 5 or above, round up. If it is below 5, round down.
[a] Example: 23 725 to the nearest 10 000 would round down to 20 000 because the thousands digit is a 3.
To round to the nearest 100 000, you look at the tens of
thousands digit. If it is 5 or above, round up. If it is below
5, round down.
Example
583 725 to the nearest 100 000 would round up to
600 000 because the tens of thousands digit is an 8.
[q] Roman Numerals
The Romans used some of the letters from the Latin
alphabet (I, V, X, L, C, D and M) to represent numbers:
[a] Example
• 5 = V, so 4 = IV (one less than 5) and 6 = VI
(one more than 5)
• 10 = X, so 9 = IX (one less than 10) and 11 = XI
(one more than 10)
• X can be placed before L to make 40 (XL) and before
C to make 90 (XC).
• C can be placed before D to make 400 (CD) and
before M to make 900 (CM).
[q] Recording Years in Roman Numerals
[a] The Romans were one of the first civilisations to use calendars, so they recorded the years using their number system.
Example
2015 would be recorded as MMXV:
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