QUESTION

# Expanded form of 78.059 is:(a) $70+\dfrac{5}{10}+\dfrac{9}{100}$(b) $70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}$(c) $70+8+\dfrac{5}{10}+\dfrac{9}{100}$(d) None of these

Hint: In this question, we first need to know about the place values of the digits after the decimal. Then expand them by expressing them as the sum of their place values.

FACE VALUE AND PLACE VALUE OF THE DIGITS:

In a numeral, the face value of a digit is the value.

In a numeral, the place value of a digit changes according to the change of its place.

In decimal representation the place just after the decimal is called tenths place. So, to get the place value of the digit we need to multiply the digit with $\dfrac{1}{10}$.

The place next to the tenths place is called the hundredths place in which we need to multiply the digit by $\dfrac{1}{100}$ to get the place value of the corresponding digit.

The place next to the hundredths place is called the thousandths place in which we need to multiply the digit by $\dfrac{1}{1000}$ to get the place value of that digit.

As we already know the place before the decimal is ones and the one before it is tens and so on.

Now, given in the question 78.059

Here, 7 is present in the tens place. So, the place value of 7 is

$7\times 10$

Now, there are 8 in the one place whose place value can be represented as.

$8\times 1$

Now, in the tenths place there is 0 whose place value can be represented as.

$0\times \dfrac{1}{10}$

There is 5 in the hundredths place whose place value will be.

$5\times \dfrac{1}{100}$

Now, in the thousandths place there is 9 whose place value is given by.

$9\times \dfrac{1}{1000}$

Now, adding these all place values gives us the number which is also its expanded form.

\begin{align} & \Rightarrow 78.059=7\times 10+8\times 1+0\times \dfrac{1}{10}+5\times \dfrac{1}{100}+9\times \dfrac{1}{1000} \\ & \therefore 78.059=70+8+0+\dfrac{5}{100}+\dfrac{9}{1000} \\ \end{align}

Hence, the correct option is (b).

Note: It is important to note that the place value of the digit just after the decimal will be tenths unlike the ones digit just before the decimal.

It is also to be noted that there is a zero present in the tenths place and 5 in the hundredths place which should be represented accordingly because neglecting the zero and considering the 5 as tenths place gives us a complete wrong result.

While representing the expanded form we need to consider all the place values of the digits and should not interchange any of the digits because it changes the place value completely. Then add them accordingly.