Download number and place value

WJEC MATHEMATICS
INTERMEDIATE
NUMBER
NUMBER AND PLACE VALUE
1
Contents
Writing numbers as words
Writing words as numbers
Rounding to the nearest 10, 100, 1000
Rounding to the nearest whole number (integer)
Rounding to the nearest decimal place
Rounding to the nearest significant figure
Directed Numbers
Estimation
Rounding in Context
Credits
WJEC Question bank
http://www.wjec.co.uk/question-bank/question-search.html
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Writing numbers as words and words as numbers
Exam Questions N1
1.
2.
3.
4.
5.
6.
Exercise N1
a. Write 14608 in words
b. Write eighteen thousand and four in figures
c. Write seven thousand and forty four is figures
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Rounding to the Nearest 10, 100, 1000
To round to the nearest multiple of ten, follow these steps:
• Underline the tens digit
• Look at the units digit
o If this number is 5, 6, 7, 8, or 9, round the tens digit up by
one
o If this number is 0, 1, 2, 3, or 4 then the tens digit stays
the same
• The units column becomes zero
Example
4
To round to the nearest hundred, follow these steps:
• Underline the hundreds digit
• Look at the tens digit
o If this number is 5, 6, 7, 8, or 9, round the hundreds digit
up by one
o If this number is 0, 1, 2, 3, or 4 then the hundreds digit
stays the same
• The units and tens column becomes zero
Example
5
To round to the nearest thousand, follow these steps:
• Underline the thousand digit
• Look at the hundreds digit
o If this number is 5, 6, 7, 8, or 9, round the thousands digit
up by one
o If this number is 0, 1, 2, 3, or 4 then the thousands digit
stays the same
• The units, tens, and hundreds column becomes zero
Example
6
Exercise N2
1. Round the following numbers to the nearest 10
a. 46
d. 152
g. 4153
b. 84
e. 684
h. 1354
c. 35
f. 354
i. 7
2. Round the following numbers to the nearest 100
a. 153
d. 105
g. 196
b. 751
e. 4568
h. 5464
c. 998
f. 15746
i. 454
3. Round the following numbers to the nearest 1000
a. 4564
d. 15421
g. 79452
b. 7831
e. 1527
h. 8821
c. 1321
f. 15434
i. 2521
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Exam Questions N2
1.
2.
3.
4.
5.
6.
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Rounding to the nearest number (integer)
In maths, an integer is a number without any decimal places (a
whole number). To round any number to the nearest integer follow
these steps:
• Look at the first decimal place
o If this number is a 5, 6, 7, 8, or 9, round the units digit up
by one
o If this number is a 0, 1, 2, 3, or 4, the units digit remains
the same.
• Make sure your answer has no decimal places
Example
9
Exercise N3
Round the following to the nearest integer
a. 12.5
b. 56.9
c. 45.56
d. 11.52
e. 1.3
f. 7986.32
g. 145.74
h. 123.41
i. 0.7
Exam Questions N3
1.
2.
3.
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Rounding to a number of decimal places
If you are asked to round to one decimal place, underline the first
decimal place. If you are asked to round to two decimal places,
underline the second.
Here's an example to consider as we go...
Now, look at the digit to the right of your underlined number.
• If this number is a 5, 6, 7, 8, or 9, round the underlined number
up by one
• If this digit is a 0, 1, 2, 3, or 4, the underlined number stays the
same
Write the number out again, but don't write any numbers after the
underlined number
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Exercise N4
1. Round the following numbers to 1 decimal place
a. 12.35
d.45.45
g. 784.598
b. 54.21
e. 54.54
h. 483.99
c. 15.22
f. 103.54
i. 7.589
2. Round the following numbers to 2 decimal places
a. 15.564
d. 7.85431
g. 1.245
b. 12.359
e. 32.1394
h. 3.547
c. 1.2568
f. 4.5848
i. 0.125
3. Round the following numbers to 3 decimal places
a. 0.31546
d. 7.35421
g. 1.25468
b. 0.31456
e. 765.3659
h. 0.00215
c. 0.11245
f. 12.524981
i. 0.0009
Exam Questions N4
1.
Note: Rounding to decimal places is usually asked at the end of
other questions
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Rounding to a number of Significant figures
Zero is not significant... Aw... :(
This means, all other numbers are significant! Yay!
When questions ask you to round to a number of significant figures,
count from the left the number that you need. This will be the point
to which you round.
Example 1
Look back in this booklet to learn how to round to the nearest 1000.
The answer here would be 546000
Example 2
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Look back in this booklet to learn how to round to decimal places.
The answer here would be 0.015
Important note: Once you have found the first significant figure,
all zeros to the right of it are now significant! It's like magic!
Exercise N5
Complete the following table:
Again, this topic may be on the end of any other question so make
sure you learn this! For exam questions on this topic see the USING
A CALCULATOR BOOKLET.
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Directed Numbers (Positive and Negative)
If a number doesn't have a sign in front of it, it is a positive number.
Adding a positive
Adding a positive number will work up the number line (to the right).
This is the most basic form of adding.
e.g.
3+5=8
-5 + 4 = -1 (Start at -5 and move 4 to the right)
Adding a negative
Adding a negative will move you down the number line (to the left)
e.g.
9 + (-4) = 5 (Start on 9 and move 4 to the left)
e.g.
-4 + (-3) = -7 (Start on -4 and move 3 to the left)
Subtracting a positive
Similarly, subtracting a positive will move you down the number line
e.g.
10 - 5 = 5 (Start at 10 and move 5 to the left)
e.g.
-6 - 4 = -10 (Start at -6 and move 4 to the left)
Subtracting a negative
This is the one that catches everyone out! Subtracting a negative will
move you up the number line (to the right)
e.g.
5 - (-3) = 8 (Start on 5 and move 3 to the right)
e.g.
-5 - (-3) = -2 (Start on -5 and move 3 to the right)
So, when two minus signs are next to each other, they are an add!!!
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Exercise N6
1. Calculate the following
a. 5 - 7
f. - 5 - 3
k. 9 - ( - 2)
b. 4 + 6
g. - 6 + 7
l. - 4 - ( - 5)
c. 13 + 5
h. 5 + (- 6)
m. - 6 - ( - 2)
d. 6 - 3
i. 4 + (- 8)
n. - 12 - ( - 12)
e. - 4 + 6
j. 7 - ( - 4)
o. 9 - ( - 5) - ( -3)
Multiplying / dividing positives
Multiplying, or dividing, two positive numbers will give you a positive
number.
e.g.
5 x 5 = 25
Multiplying / dividing one positive and one negative
When you multiply, or divide, one positive and one negative, your
answer will be negative.
e.g.
-5 x 3 = -15
e.g.
7 x -7 = -49
Multiplying / dividing two negatives
When you multiply, or divide, two negatives, your result will be
positive!!
e.g.
- 5 x - 10 = 50
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Exercise N7
a. 5×−3
f. 8×−6
k. 12×−7
b. 6×7
g. 5×−2
l. −9×−7
c. 9×12
h. 6×−4
m.−10 ×−11
d. 8×6
i. 7×−1
n. −7×−12
e. 4×3
j. 3×−9
o. −4×−1
Estimation
If we are in a hurry and need to know the approximate value of
something we need to estimate.
KEY POINT - When you estimate, round all
numbers to ONE SIG FIG
Example
Estimate:
3.96×195
39.75
Rounding each of these values to 1 significant figure.
4×200
40
800
=
40
= 20
Important!
If you are asked to estimate and you work it out
exactly you get no marks. So be careful!
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Exam Questions N5
1.
See 'Powers and
Roots' if you are
unsure of this
2.
notation
3.
4.
5.
6.
7.
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Rounding in Context
Earlier in this booklet we learnt the rules of rounding, however
sometimes we need to break these rules.
Example
A group of 100 university students book a trip. They need to know
how many buses to book (a bus can hold 45 people).
100
45
= 2.22
We cannot hire 2.22 buses so we need to round our answer. 2.22,
as we have already learnt, rounds to 2. However, if they hired two
buses, that's only 2×45 = 90 seats - That's 10 people who cannot
go.
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑢𝑠𝑒𝑠 =
So, due to the context of this, we need to round UP to 3 buses.
This is an example of rounding up or down depending on the
question.
Exam Question N6
1.
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