Question

The correct expanded form for $2.06$ is ___________
A.$(2 \times 10) + (6 \times 100\;{\text{ )}}$
B.$(2 \times 1) + (6 \times 10\;{\text{ )}}$
C.$(2 \times 10) \div (6 \times100 \;{\text{ )}}$
D.$(2 \times 1) + (6 \div100 \;{\text{ )}}$

Answer 1

Hint: When we write a number in the expanded form, we write the terms using addition, multiplication and the division. Take the given number and do its expansion in the form of the given options.

Complete step-by-step answer:
Take the given number: $2.06$
The above number can be expanded as –
$2.06 = 2 + 0.06$
Use the multiplicative identity which states that when any number “a” is multiplied with it, give the value as the number itself.
$2.06 = \left( {2 \times 1} \right) + 0.06$
Convert the decimal point in the form of fraction. To convert decimal into fraction, place the decimal number over its place value. For example, for $0.6$ the six is in the tenths place so that we place $6$ over $10$ to create the equivalent fraction i.e. $\dfrac{6}{{10}}$ and similarly if there is two digits after decimal point, for $0.06$ the six is in the hundredths place so that we place $6$ over $100$ to create the equivalent fraction i.e. $\dfrac{6}{{100}}$.
So, the above expression can be re-written as –
 \[2.06 = \left( {2 \times 1} \right) + \left( {\dfrac{6}{{100}}} \right)\]
Fraction is the number expressed in the form of the numerator to the denominator. It can be written as division. Here $\dfrac{6}{{100}}$ can be expressed as $6 \div 100$
 \[ \Rightarrow 2.06 = \left( {2 \times 1} \right) + \left( {6 \div 100} \right)\]
So, the correct answer is “Option D”.

Note: Fractions are the part of the whole. Generally it represents any number of equal parts and it describes the part from a certain size and expressed in the form of numerator upon denominator. In the fraction, in denominator if we have ten then while converting into decimal point shift one point from right and similarly if there is hundred then shift two points from the right.