First Edition
Form I Math
Traf Math I
Lorem Ipsum Dolor Facilisis
Notations
1
Trafalgar School’s Math
Ebook.
Section 1
Notations
This is an electronic textbook for Secondary One Mathematics.
It has been created and collated by Jennifer Robinson and
Greg Scruton.
Online Resources include the Trafalgar Math Website
and Greg Scruton’s Form I Math blog
Jennifer Robinson and Greg Scruton also have portal pages
which are important resources for this text.
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Place Value
Literal notation of powers of ten can define the position or place of a digit in a number. That is to say that knowing the place of a number we can
tell where in a number a digit is placed.
M OVIE 1.1 Place Value and Face Value Notes Video
For example, in the number 127
500 the digit 7 is in the thousands place or we can say that the place value of the 7 is the thousands
place.
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In the chart below each of the places between the hundred millions place and the millionths place are shown.
Examples:
1. Find the place value of the 5 in the chart.! !
2. Find the place value of the 6 in the chart.!
! !
Face Value
The face value of a selected numeral in a number is that of the numeral itself:
Examples:
1. Find the face value of the underlined numeral: 12 345 678!
2. Find the face value of the underlined numeral: 48 730.09 33
!
4
Exer-
cises:
Find
the
face
and
place
values of
the
underlined
digits.
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Number Notations
Power of Ten
Numerical!
Exponential!
Literal!
Fractional
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7
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Expanded Notation
Expanded notation using powers of ten (see Figure 3: Powers of 10)
Expanded Notation Math Program
M OVIE 1.2 Expanded Notation Notes Video
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Expanded Notation Exercise 1:
Convert the following numbers into expanded notation.
1. 430337.0841!
!
!
2. 8848.60651!!
!
!
3. 350823.0705!
!
!
4. 170014.0097
5. 433109.35! !
!
!
6. 910773.125!!
!
!
7. 14894.78001!
!
!
8. 27887.56704
9. 895584.4919!
!
!
10. 21762.1209!
!
!
11. 250203.0019!
!
!
12. 706630.48028
13. 4749.0713!!
!
!
14. 996923.75602! !
!
15. 948835.0162!
!
!
16. 21036.5912
17. 80842.09747!
!
!
18. 460974.8005!
!
19. 537721.45698! !
!
20. 54165.326
!
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Expanded Notation Exercise 2:
Convert the following numbers into expanded notation
1. 126923.4205!
!
!
!
2. 1351.66152!!
!
!
3. 558038.01309!
!
!
!
4. 52867.903
5. 503605.15924!
!
!
!
6. 539636.618!!
!
!
7. 24370.50002!
!
!
!
8. 95611.39008
9. 54515.044! !
!
!
!
10. 888.50709!!
!
!
11. 956690.8245!
!
!
!
12. 14569.6543
13. 5319.674! !
!
!
!
14. 644.22!
!
!
!
15. 57300.18387!
!
!
!
16. 434594.2111
17. 5040.073! !
!
!
!
18. 8293.4329!!
!
!
19. 8620.7701!!
!
!
!
20. 60768.00074
21. 9817.907! !
!
!
!
22. 260277.01652! !
!
23. 8620.148! !
!
!
!
24. 4122.767
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Literal Notation
Converting Numbers to Words (Standard to Literal)
M OVIE 1.3 Literal Notation Notes Video 1
M OVIE 1.4 Literal Notation Notes Video 1
Converting words to numbers
Converting numbers to words
Literal Notation Math Program
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Notice that when numbers are written, spaces are used between specific places: billions and hundred millions, millions and hundred thousands,
thousands and hundreds, then there is a decimal place between the ones and the tenths.
The spaces help us to identify place values, and to quickly be able to read the number.
To convert a number that does not have any decimal places, first you must be able to read numbers up to and including the
hundreds.
Note: The spaces are not obligatory, they are a means to help identify the place values quickly.
Example I:
135 One hundred thirty-five
91
Ninety-one
201 Two hundred one
When reading numbers into the thousands (thousands to hundred thousands place) place, read the numbers normally (as if they are 1 to 999),
then put the word thousand after them, and continue with hundreds, tens and ones.
Example 2:
8 241 Eight thousand two hundred forty-one
71 470 Seventy-one thousand four hundred seventy
789 517 Seven hundred eighty-nine thousand five hundred seventeen
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900 012 Nine hundred thousand twelve
When reading numbers into the millions (million to hundred million) place, read the numbers normally (as if they are 1 to 999), then put the word
million after them, and continue with thousands, hundreds, tens and ones.
Example 3:
7 529 121 Seven million five hundred twenty-nine thousand one hundred twenty-one
19 100 913 Nineteen million one hundred thousand nine hundred thirteen
275 102 715 Two hundred seventy-five million one hundred two thousand seven hundred fifteen
When reading numbers between one and zero or decimal numbers we:
!
a. read the number after the decimal point normally,
!
b. when finished reading the number, read the last digits place value.
Examples
0.5 Five tenths.
0.12 Twelve hundredths.
0.237 Two hundred thirty-seven thousandths.
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0.009 Nine thousandths.
0.1249760 One million two hundred forty-nine thousand seven hundred sixty ten millionths.
Suggested spacing after decimals:
Space the numbers after the decimal place as if the decimal place did not exist or the way we space numbers before the decimal place.
Example 1: 0.127936
It is hard to read 0.127936 but if we space it like this: 0.127 936, we can read it much easier as
one hundred twenty seven thousand nine hundred thirty-six millionths.
Example 2: 0.9398772
if we space this way 0.9 398 772 we can now read it as
nine million three hundred ninety-eight thousand seven hundred seventy-two ten millionths.
Reading numbers greater than one and with decimals:
a. read the whole number part normally,
b. read the decimal as “and”,
c. read the decimal part
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Example 1:
126 749.264 936
One hundred twenty-six thousand seven hundred forty-nine and two hundred sixty-four thousand nine hundred thirty-six millionths.
Example 2:
6 413 559.269
Six million four hundred thirteen thousand five hundred fifty-nine and two hundred sixty-nine thousandths.
Converting Numbers to Words Exercise 1:
1) 3.52103!
!
!
!
2) 8.03!
5) 350602.00009!
!
!
9) 548302.006! !
!
13) 79857!!
!
!
3) 968037.237! !
!
!
4) 8708.35748
6) 17028.000009!
!
!
7) 91.15! !
!
!
!
8) 292415.5829
!
10) 4822.00073!
!
!
11) 1126.099! !
!
!
12) 1176145
!
!
14) 7.9032!
!
!
!
15) 7852.6243! !
!
!
16) 491892.00045
17) 463859.00003! !
!
18) 6559.89035!
!
!
19) 7.995!!
!
!
20) 411750.00008
!
!
!
!
Answers
1) three and fifty-two thousand one hundred three hundred thousandths
2) eight and three hundredths
3) nine hundred sixty-eight thousand thirty-seven and two hundred thirty-seven thousandths
4) eight thousand seven hundred eight and thirty-five thousand seven hundred forty-eight hundred thousandths
5) three hundred fifty thousand six hundred two and nine hundred thousandths
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6) seventeen thousand twenty-eight and nine millionths
7) ninety-one and fifteen hundredths
8) two hundred ninety-two thousand four hundred fifteen and five thousand eight hundred twenty-nine ten thousandths
9) five hundred forty-eight thousand three hundred two and six thousandths
10) four thousand eight hundred twenty-two and seventy-three hundred thousandths
11) one thousand one hundred twenty-six and ninety-nine thousandths
12) one million one hundred seventy-six thousand one hundred forty-five
13) seventy-nine thousand eight hundred fifty-seven
14) seven and nine thousand thirty-two ten thousandths
15) seven thousand eight hundred fifty-two and six thousand two hundred forty-three ten thousandths
16) four hundred ninety-one thousand eight hundred ninety-two and forty-five hundred thousandths
17) four hundred sixty-three thousand eight hundred fifty-nine and three hundred thousandths
18) six thousand five hundred fifty-nine and eighty-nine thousand thirty-five hundred thousandths
19) seven and nine hundred ninety-five thousandths
20) four hundred eleven thousand seven hundred fifty and eight hundred thousandths
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Fractional Notation
M OVIE 1.5 Fraction Notation Notes Video
Fractional notation in mathematics is where you have a fraction written in
the form:
The front number (w) is called the whole number,
the top number (n) is called the numerator and
the bottom number (d) is called the denominator.
For example 2.3 can be read as two and three tenths. Notice that two is a
whole number, and that three tenth is a fraction where the numerator is 3
and the denominator is 10.
When reading numbers between one and zero or decimal numbers we:
a. The number before (left of) the decimal point becomes the whole number
b. The number after (right of) the decimal point becomes the numerator
c.The last digit’s place value becomes the denominator.
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Examples:
1. Convert the following number into fractional form: 1 567.34
2. Convert the following number into fractional form: 65.0954!
!
!
3. Convert the following number into fractional form: 7.006
Fractional Notation Exercise 1: Express the following numbers in fractional notation or standard notation.
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Exercise: Standard, Expanded, Literal (Word) & Fractional Form!
Convert each given number into the three other missing forms. The first one is completed as an example.
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Exercise 2:
Convert the following into the three missing forms: either standard form, expanded notation, literal form, or fractional form.
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