What is Hundredth?

You may have seen price tags of some items as Rs.450.60, Rs. 3445.90, etc. When you buy vegetables in a nearby shop, you can see the weight of vegetables as a decimal in the digital weighing machine. At a fuel filling station, you can see the volume of petrol filled as numbers like 3.81 litres. These numbers with whole numbers and fractional values are called decimal numbers. A hundredth of something means one of a hundred equal parts of that thing. Let us understand about the hundredth value of a decimal in this article.

Definition of Hundredth

The hundredth is the place value of the digit that appears after the tenths and before the one-thousandth digit of a decimal. For example,

\[1\] m = \[100\] cm

\[1\] cm = \[1/100\] m = \[0.01\]m

Thus, \[1\] cm is one-hundredth of a metre.

Place Value Chart for Tenth, Hundredth and Thousandth

The place value chart for decimal numbers has been represented by the image below.

Place Value Table

Comparison of Decimals and Fractions

Two-Tenths in Decimal Form

The value of two-tenths is \[2/10 = 0.2\]. Two-tenths of a number is calculated by multiplying the number by \[0.2\].

For example, two-tenths of 100 is \[\dfrac{2}{{10}}\times\,100 = 0.2\,\times \,100\, = \,20\].

Writing Fractions in the Form of Decimals

The two parts of a fraction are the numerator and the denominator. A fraction can be converted to a decimal by converting the denominator into a multiple of \[10\].

Step \[1\]: Identify a number to multiply with a denominator to get a number that can be \[\] \[10,\,10,\,100\,...\].

Step\[2\]: Multiply the number with both the numerator and denominator.

Step\[3\]: Write the number to the right-hand side of the decimal point based on the number of zeroes in the denominator.

Use this common method: \[2/10 = 0.2\], \[2/100 = 0.02\], \[2/1000 = 0.002\].

For example, \[\dfrac{2}{5} = \dfrac{{2\,\times\,2}}{{5\,\times \,2}} = \dfrac{4}{{10}} = 0.4\].

Interesting Facts

• Every fraction can be a decimal but every decimal cannot be a fraction.

• The golden ratio is a decimal. Its approximate value is \[1.618\].

• Decimals are also used in percentages. For example, standardised milk has a fat percentage of \[4.5\,\% \].

Solved Problems

1. Find the hundredth of the following numbers

1. 4.36

Ans: 4.36. The hundredth place is 6.

2. 2.987

Ans: 2.987. The hundredth place is 8.

3. 5.46

Ans: 5.46. The hundredth place is 6.

4. 9.21

Ans: 9.21. The hundredth place is 1.

2. Write the following numbers in the place value table.

1. 3.65

2. 2.67

3. 32.56

4. 112.64

Ans:

3. Write the following as decimals:

(a) Nine ones and one-hundredth

(b) Twenty and four-hundredth

Ans:

(a) Nine ones and one-hundredth

Nine ones \[ = 9\,\times\,1 = 9\]

One-hundredth \[ = 1/100 = 0.01\]

Thus, the required decimal number is: \[9{\rm{ }} \times {\rm{ }}1{\rm{ }} + {\rm{ }}1/100{\rm{ }} = {\rm{ }}9{\rm{ }} + {\rm{ }}0.01{\rm{ }} = {\rm{ }}9.01\]

\[{\rm{9 }}\times{\rm{ }}1{\rm{ }} + {\rm{ }}1/100{\rm{ }} = {\rm{ 9 }} + {\rm{ }}0.01{\rm{ }} = {\rm{ 9}}.01\]

(b) Twenty and four-hundredth

Twenty – \[20\]

Four-hundredth = \[\dfrac{4}{100} = 0.04\]

Therefore, the required decimal is: \[20 + 0.04 = 20.04\]

Applications of Decimals in Daily Life

• The use of decimals helps in performing calculations accurately.

• Decimals are useful in calculations related to money.

• They are useful in measuring objects.

Practice Questions

1. Find the hundredth of the following numbers.

1. 2.78

2. 3.21

3. 9.349

4. 0.45

Answer: a) 8, b) 1, c) 4, d) 5

2. Write the following as decimals.

1. Six ones and four-hundredth

2. Three-hundredth

Answer: a) 6.04, b) 0.03

Conclusion

Decimals are very essential in calculations performed in various fields. In this article, we learned the definition of the hundredth in a decimal, the difference between a decimal and a fraction, writing a decimal number in a place value chart and finding the hundredth in a decimal with examples.