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Multiplication by 10; 100 and 1,000
\latex{10}
\latex{\times}
How much money would you have if the Financial Fairy multiplied every banknote and coin by ten?
When converting units or dealing with money, you often need to multiply amounts by \latex{ 10 }, \latex{ 100 } or \latex{ 1,000 }. The place value table below will help you with this.
thousands
hundreds
tens
ones
\latex{ 5 }
\latex{ 0 }
\latex{ 5 }
\latex{ 0 }
\latex{ 0 }
\latex{ 5 }
\latex{ 0 }
\latex{ 0 }
\latex{ 0 }
\latex{ 5 }
\latex{5 \times 1 = \textbf{\textcolor{#ff0000}{5}}}
\latex{5 \times 10 = \textbf{\textcolor{#ff0000}{50}}}
\latex{5 \times 100 = \textbf{\textcolor{#ff0000}{500}}}
\latex{5 \times 1,000 = \textbf{\textcolor{#ff0000}{5,000}}}
x \latex{ 1,000 }
x \latex{ 100 }
x \latex{ 10 }
As you can see from the table, the place value of \latex{ 5 } changes during multiplication.
\latex{\times 10}
\latex{\times 10}
\latex{\times 100}
When multiplying a natural number by \latex{ 10 }, each digit moves up one place value.
(The unit digit becomes \latex{ 0 }.)
(The unit digit becomes \latex{ 0 }.)
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{\times \;10 =}
\latex{3\textcolor{#ff0000}{7}4 \times 10 = 3,\textcolor{#ff0000}{7}40}
tens
hundreds
When multiplying a natural number by \latex{ 100 }, every digit moves up two place values.
(The unit and ten digits become \latex{ 0 }.)
(The unit and ten digits become \latex{ 0 }.)
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{\times \;100 =}
\latex{ 0 }
\latex{3\textcolor{#ff0000}{7}4 \times 100 = 3\textcolor{#ff0000}{7},400}
tens
thousands
When multiplying a natural number by \latex{ 1,000 }, every digit moves up three place values.
(The unit, ten and hundred digits become \latex{ 0 }.)
(The unit, ten and hundred digits become \latex{ 0 }.)
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 3 }
\latex{ 7 }
\latex{ 4 }
\latex{ 0 }
\latex{\times \;1,000 =}
\latex{ 0 }
\latex{ 0 }
\latex{3\textcolor{#ff0000}{7}4 \times 1,000 = 3\textcolor{#ff0000}{7}4,000}
tens
ten thousands
Example
Do the following multiplications.
a) \latex{\text{ }16 \times 300;}
b) \latex{\text{ }5 \times 25 \times 8 \times 125 \times 2 \times 4.}
Solution
The properties of multiplication can help you with the calculations.
\latex{\text{a) }16 \times 300 = 16 \times (3 \times 100) = (16 \times 3) \times 100 = 48 \times 100 = 4,800;}
\latex{\text{b) } 5 \times 25 \times 8 \times 125 \times 2 \times 4 = \left(5\times2\right) \times\left(25\times4\right) \times\left(125\times8\right) = 1,000,000 .}
\latex{ 10 }
\latex{ 100 }
\latex{ 1,000 }
\latex{300 = 3 \times 100}
\latex{2 \times 5 = 10}
\latex{4 \times 25 = 100}
\latex{8 \times 125 = 1,000}
Exercises
{{exercise_number}}. Convert the following lengths into \latex{ decimetres }, \latex{ centimetres } and \latex{ millimetres }.
a) \latex{ 21\,m }
b) \latex{ 201\,m }
c) \latex{ 314\,m }
d) \latex{ 450\,m }
e) \latex{ 1,101\,m }
f) \latex{ 60\,m }
g) \latex{ 671\,m }
h) \latex{ 607\,m }
i) \latex{ 670\,m }
j) \latex{ 5,021\,m }
k) \latex{ 3,303\,m }
l) \latex{ 1,001\,m }
{{exercise_number}}. Are the following statements true or false?
a) If you write each digit of a natural number in a place value greater than one, then you have multiplied the number by \latex{ 10 }.
b) If there are exactly two zeros in a number, then that number is \latex{ 100 } times another natural number.
c) If you multiply a natural number by \latex{ 10 }, it ends in exactly one zero.
d) If you multiply a natural number by \latex{ 100 }, it ends in at least two zeros.
b) If there are exactly two zeros in a number, then that number is \latex{ 100 } times another natural number.
c) If you multiply a natural number by \latex{ 10 }, it ends in exactly one zero.
d) If you multiply a natural number by \latex{ 100 }, it ends in at least two zeros.
{{exercise_number}}. When you see the expression \latex{ 1 } : \latex{ 1,000,000 } on a map, it means that \latex{ 1\,cm } on the map is \latex{ 1,000,000\,cm } in reality. How many \latex{ kilometres } is Gibraltar from Tangier? Use a piece of string to measure it on the map given. (→)
{{exercise_number}}. The following numbers are one hundred times and ten times what number?
a) \latex{ 7,000 }
b) \latex{ 14,000 }
c) \latex{ 3,600,000 }
d) \latex{ 0 }
Quiz
Ten times a natural number multiplied by a hundred is equal to a million times the number. What number is that?
