Question

Prove that “ The place value of a digit at the hundredths place is \[\dfrac{1}{{10}}\] times the same digit at the tenths place.”

Answer 1

Hint: Each digit in a number has a place value in mathematics. The meaning expressed by a digit in a number based on its location in the number is known as place value. The places are generally called tenth, hundredth, thousandth, lakhs/millions etc. depending on the number system followed.
The given question can be solved by forming an equation from the given data.

Complete step-by-step answer:
A mathematical expression containing the equals symbol is known as an equation. Algebra is often used in equations. The tens place of a digit is obtained by multiplying it by \[10\] .Similarly, the hundredths place of the digit is obtained by multiplying it with \[100\] and so on.
Let us form an equation to solve the given sum:
Let \[x\] be the digit at tenths and hundredths place of the given number.
The place value of the digit at the tens place will be-
 \[10x\]
In the same manner the place value at the hundredths place will be-
 \[100x\]
Now it is given that
 \[\dfrac{1}{{10}}\] Place Value at hundredths place= Place value at tenths place
Comparing it with the given formula and variables, we get,
 \[\dfrac{1}{{10}} \times 100x = 10x\]
Dividing the RHS, we can conclude that both sides of the equation will be equal.
 \[10x = 10x\]
Hence it is proved that “The place value of a digit at the hundredths place is \[\dfrac{1}{{10}}\] times the same digit at the tenths place.”

Note: In order to solve such questions, one should define the missing variable with alphabets such as \[a,b,c,x,y,z\] etc and form an equation from the data given.
Cross check the final answer obtained with simple multiplication and other operators as required. In the given sum, we can cross verify that \[10 = \dfrac{1}{{10}}100\] and hence satisfies the given condition.