How to Identify and Use Hundredths in Everyday Problems
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
4.36
Ans: 4.36. The hundredth place is 6.
2.987
Ans: 2.987. The hundredth place is 8.
5.46
Ans: 5.46. The hundredth place is 6.
9.21
Ans: 9.21. The hundredth place is 1.
2. Write the following numbers in the place value table.
3.65
2.67
32.56
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.
2.78
3.21
9.349
0.45
Answer: a) 8, b) 1, c) 4, d) 5
2. Write the following as decimals.
Six ones and four-hundredth
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.
FAQs on Understanding Hundredths in Maths
1. What does a 'hundredth' mean in Mathematics?
In Mathematics, a 'hundredth' represents one part of a whole that has been divided into 100 equal parts. For instance, if you divide a cake into 100 equal slices, one single slice is one-hundredth of the entire cake. It is the second place value to the right of the decimal point.
2. How can you write one-hundredth as a fraction and as a decimal?
One-hundredth can be expressed in two common forms:
- As a fraction: It is written as 1/100.
- As a decimal: It is written as 0.01.
3. Where is the hundredths place located in a decimal number?
In a decimal number, the hundredths place is the second digit to the right of the decimal point. For example, in the number 5.28, the digit '8' is in the hundredths place, representing eight-hundredths.
4. What is the difference between a tenth and a hundredth?
The key difference is the number of equal parts a whole is divided into. A tenth (0.1) means the whole is divided into 10 equal parts, while a hundredth (0.01) means the whole is divided into 100 equal parts. This makes a tenth ten times larger than a hundredth (0.1 = 0.10).
5. Can you provide some real-world examples of where hundredths are used?
Hundredths are frequently used in everyday life, especially in contexts requiring precision. Key examples include:
- Money: In India, one paisa is one-hundredth of a rupee (₹0.01). So, 50 paise is 50-hundredths of a rupee.
- Measurements: One centimetre is one-hundredth of a metre (0.01 m).
- Percentages: A percentage is another way to express hundredths. For example, 45% means 45 out of 100, or 45-hundredths.
6. Why is the number 0.75 read as 'seventy-five hundredths'?
The number 0.75 is read as 'seventy-five hundredths' because it represents the sum of 7 tenths and 5 hundredths. Since 7 tenths is equal to 70 hundredths (7/10 = 70/100), when you add the 5 hundredths, you get a total of 75 hundredths (70/100 + 5/100 = 75/100). This name accurately describes its value as a fraction of 100.
7. How do you convert a fraction with a denominator of 100 into a decimal?
To convert a fraction with 100 as its denominator into a decimal, you write the numerator and place the decimal point two places from the right. For example, the fraction 37/100 becomes 0.37. If the numerator is a single digit, like in 6/100, you add a zero as a placeholder to make it 0.06.
