Question

Write the following decimal numbers in expanded form
$1234.56 = 1000 + 200 + 30 + 4 + \dfrac{5}{{10}} + \dfrac{6}{{100}}$
A.True
B.False

Answer 1

Hint: The expanded form for decimal numbers is the notation or mathematical expression by which the sum of the values of each digit in the number is shown. Multiply the numbers with their place value and add them to get the expanded form.

Complete step-by-step answer:
The given number is $1234.56$ .
We have to write its expanded form. We use a place value system to write it. The place value tells the value of the digit in a number.
We know the place value of a digit at one’s place is $1$ , tens place is $10$, hundred place is $100$ and thousands place is $1000$. The place value of the numbers after decimal are-
Place value of digit at tenth place=$\dfrac{1}{{10}}$
Place value of digit at hundredth place=$\dfrac{1}{{100}}$
We multiply the numbers with their place value and add them to write in expanded form.
So here the place value of $4$ is $1$ .The place value of $3$ is$10$. The place value of $2$ is $100$.The place value of $1$ is $1000$.The place value of $5$ is$\dfrac{1}{{10}}$. The place value of $6$ is$\dfrac{1}{{100}}$.
Then we can write –
$ \Rightarrow 1234.56 = \left( {1 \times 1000} \right) + \left( {2 \times 100} \right) + \left( {3 \times 10} \right) + \left( {4 \times 1} \right) + \left( {5 \times \dfrac{1}{{10}}} \right) + \left( {6 \times \dfrac{1}{{100}}} \right)$
On simplifying we get,
$ \Rightarrow 1234.56 = 1000 + 200 + 30 + 4 + \dfrac{5}{{10}} + \dfrac{6}{{100}}$
Hence the statement is correct.
Answer- The correct answer is A.

Note: The expanded form of decimal number is written with a base $10 - $multiple denominator. The decimal positional system was invented by Archimedes to represent large numbers which were multiples of $10$.We use decimal numbers everyday in life in-
1.Measuring length.
2.Measuring weight.
3.Measuring money in dollars and penny.