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Decimal numbers
Example
Expand the fractions so that their denominators are \latex{ 10 }; \latex{ 100 }; \latex{ 1,000 }.
a) \latex{\frac{1}{2}}
b) \latex{\frac{3}{4}}
c) \latex{\frac{171}{125}}
Solution
a) \latex{\frac{1}{2} =\frac{5}{10}}
b) \latex{\frac{3}{4} =\frac{75}{100}}
c) \latex{\frac{171}{125} =\frac{1368}{1000}=1\frac{368}{1000}}
Fractions with a denominator of \latex{ 10 }; \latex{ 100 }; \latex{ 1,000 } can be written as decimal numbers.
a) \latex{\frac{5}{10} =0.5}
b) \latex{\frac{75}{100} =0.75}
c) \latex{1\frac{368}{1000}= 1.368}
The position of decimals in the place value table
In the decimal system, one step to the left corresponds to ten times the place value, and one step to the right corresponds to one-tenth of the place value. If you continue moving to the right after the unit place digit, you reach values of less than one. These values are called tenths, hundredths, ten-thousandths, hundred-thousandths, millionths, and so on.
...
hundreds
tens
units
tenths
hundredths
thousandths
...
a)
b)
c)
\latex{ 5 }
\latex{ 0 }
\latex{ 7 }
\latex{ 3 }
\latex{ 8 }
\latex{ 0 }
\latex{ 2 }
\latex{ 0 }
\latex{ 9 }
\latex{ 6 }
\latex{ 2 }
\latex{ 5 }
Expanded form
Mixed number form
Decimal form
\latex{7 \times 10 + 3 \times 1 + 2 \times \frac{1}{10}}
\latex{73 \frac{2}{10}}
\latex{73.2}
\latex{5 \times 100 + 0 \times 10 + 8 \times 1 + 0 \times \frac{1}{10} + 6 \times \frac{1}{100} }
\latex{508 \frac{6}{100} }
\latex{508.06}
\latex{0 \times 1 + 9 \times \frac{1}{10} + 2 \times \frac{1}{100} + 5 \times \frac{1}{1000}}
\latex{ \frac{925}{1000} }
\latex{0.925}
=
=
=
=
=
=
decimal
\latex{ 508 . 06 }
whole
number part
number part
fraction
part
part
decimal point
When writing decimal numbers, the decimal point separates the whole number part from the fractional part. The digits after the decimal point are called the fractional part. For numbers greater than \latex{ 0 } but less than \latex{ 1 }, you should write a \latex{ 0 } before the decimal point.
Reading out decimal numbers
the decimal number
how we say the numbers before the decimal point
what we say for the decimal point
how we say the numbers after the decimal point
\latex{ 73.2 }
\latex{ 508.06 }
\latex{ 0.925 }
seventy three
five hundred and eight
zero
point
point
point
two
zero six
nine two five
Exercises
{{exercise_number}}. Write the numbers in the place value table as decimal numbers.
...
hundreds
tens
units
tenths
hundredths
thousandths
ten
thousandths
thousandths
hundred
thousandths
thousandths
millionths
...
\latex{ 9 }
\latex{ 8 }
\latex{ 2 }
\latex{ 1 }
\latex{ 7 }
\latex{ 0 }
\latex{ 3 }
\latex{ 2 }
\latex{ 0 }
\latex{ 0 }
\latex{ 5 }
\latex{ 4 }
\latex{ 0 }
\latex{ 0 }
\latex{ 1 }
\latex{ 4 }
\latex{ 7 }
\latex{ 3 }
\latex{ 0 }
\latex{ 4 }
\latex{ 0 }
\latex{ 5 }
\latex{ 4 }
\latex{ 7 }
\latex{ 5 }
\latex{ 4 }
\latex{ 0 }
\latex{ 8 }
\latex{ 7 }
\latex{ 4 }
\latex{ 5 }
\latex{ 5 }
\latex{ 9 }
\latex{ 2 }
\latex{ 1 }
{{exercise_number}}. Write the following numbers in a place value table, then write them in decimal form.
a) \latex{5 \frac{3}{10}}
b) \latex{10\frac{3}{100}}
c) \latex{\frac{61}{100}}
d) \latex{200\frac{6}{10}}
e) \latex{50\frac{60}{100}}
f) \latex{60\frac{50}{1000}}
{{exercise_number}}. Write the following numbers in decimal form.
a) \latex{ 3 } point \latex{ 4 } tenths
b) \latex{ 7 } point \latex{ 96 } hundredths
c) \latex{ 157 } point \latex{ 157 } thousandths
d) \latex{ 2 } point \latex{ 51 } ten-thousandths
e) \latex{ 0 } point \latex{ 44 } millionths
f) \latex{ 10 } point \latex{ 6 } hundred-thousandths
{{exercise_number}}. Read the numbers out loud. Then write them down in the form of a place value table.
a) \latex{ 44.5 }
b) \latex{ 70.03 }
c) \latex{ 0.007 }
d) \latex{ 123.0321 }
e) \latex{ 20.00006 }
{{exercise_number}}. Write the following numbers in a place value table, then write them in decimal form.
a) \latex{ 2 } tens \latex{ + } \latex{ 5 } tenths
b) \latex{ 12 } tens \latex{ + } \latex{ 7 } tenths \latex{ + } \latex{ 5 } hundredths
c) \latex{ 2 } tens \latex{ + } \latex{ 3 } hundredths \latex{ + } \latex{ 4 } thousandths
d) \latex{ 0 } units \latex{ + } \latex{ 2 } tenths \latex{ + } \latex{ 8 } hundred-thousandths
c) \latex{ 2 } tens \latex{ + } \latex{ 3 } hundredths \latex{ + } \latex{ 4 } thousandths
d) \latex{ 0 } units \latex{ + } \latex{ 2 } tenths \latex{ + } \latex{ 8 } hundred-thousandths
{{exercise_number}}. The sum of a number is the following:
\latex{A \times 1000 + B \times 100 + C \times 10 + D \times 1 + E \times \frac{1}{10} + F \times \frac{1}{100} + G \times \frac{1}{1000}}
What numbers do the letters in the sum represent if the decimal form of the sum is
a) \latex{ 803.47 };
b) \latex{ 830.4 };
c) \latex{ 8,030.047 };
d) \latex{ 345.350 };
e) \latex{ 3,405.035 };
f) \latex{ 3,045.005 ?}
Quiz
Write the following number in a form that contains the least number of digits possible: \latex{ 0.000003 }.
