Question

Expand the form of 78.059.
a. \[78+\dfrac{5}{10}+\dfrac{9}{1000}\]
b. \[70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}\]
c. \[70+8+\dfrac{5}{10}+\dfrac{9}{100}\]
d. none of these

Answer 1

Hint: The given problem is related to representation of numbers in expanded form. In expanded form, a number is represented as a sum of the place values of the digits.

Complete step-by-step answer:
In the expanded form,we break up a number according to their place value and expand it to show the value of each digit. where, Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
Place value of a number increases from left to right by multiplication factor of 10 before decimal point and after the decimal point from right to left the place value of a number decreases by a multiplication factor of 1/10.
Given number is 78.059

The place value of tens position is 10.
The place value of units positive is 1.
The place value of one-tenth position is \[\dfrac{1}{10}\]
The place value of one-hundredth position is \[\dfrac{1}{100}\].

The place value of one-thousandth position is \[\dfrac{1}{1000}\].
Therefore, 78.059 can be written as \[\left( 7\times 10 \right)+\left( 8\times 1 \right)+\left( 0\times 1/10 \right)+\left( \dfrac{5\times 1}{100} \right)+\left( \dfrac{9\times 1}{1000} \right)\].
Therefore, the expanded form of 78.059 is \[70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}\].
Hence, the correct option is option B.


Note: Students may confuse expanded form and expanded notation. Here is the clarification
Expanded form is not the same as expanded notation. The expanded notation a number is represented as the sum of each digit in a number multiplied by its place value. In the expanded forms, we use only addition between the place value numbers and in the expanded notation we use addition and multiplication.
Expanded form of 78.059 is\[70+8+0+\dfrac{5}{100}+\dfrac{9}{1000}\].
Expanded notation of 78.059 is (\[\left( 7\times 10 \right)+\left( 8\times 1 \right)+\left( 0\times 1/10 \right)+\left( \dfrac{5\times 1}{100} \right)+\left( \dfrac{9\times 1}{1000} \right)\].