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Tenths and Hundredths - Decimal Place Value

Grade 5CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Understanding Tenths: When a whole is divided into 10 equal parts, each part is called one-tenth. It is written as 110\frac{1}{10} in fractions or 0.10.1 in decimals. Visually, if you imagine a long chocolate bar divided into 10 equal vertical strips, shading one strip represents 0.10.1.

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Understanding Hundredths: When a whole is divided into 100 equal parts, each part is called one-hundredth. It is written as 1100\frac{1}{100} or 0.010.01. Visually, imagine a large square grid of 10×1010 \times 10 small squares; shading just one tiny square represents 0.010.01.

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Decimal Place Value Chart: The decimal point separates the whole number from the fractional part. The positions to the right of the decimal point are: Tenths (110\frac{1}{10}), Hundredths (1100\frac{1}{100}), and Thousandths (11000\frac{1}{1000}). For example, in 25.3825.38, 22 is tens, 55 is ones, 33 is tenths, and 88 is hundredths.

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Relationship between Tenths and Hundredths: One tenth is equal to ten hundredths (0.1=0.100.1 = 0.10). Visually, one full column in a 100-square grid (which is 110\frac{1}{10} of the whole) contains exactly 1010 small squares (each being 1100\frac{1}{100} of the whole).

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Conversion of Units: Decimals are used to express smaller units in terms of larger units. Since 1010 mm =1= 1 cm, then 11 mm =110= \frac{1}{10} cm =0.1= 0.1 cm. Similarly, since 100100 paise =1= 1 Rupee, then 11 paisa =Rs. 1100=Rs. 0.01= \text{Rs. } \frac{1}{100} = \text{Rs. } 0.01.

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Expanded Form of Decimals: Decimals can be written as the sum of the values of each digit. For example, 4.564.56 can be expanded as 4+510+61004 + \frac{5}{10} + \frac{6}{100} or 4+0.5+0.064 + 0.5 + 0.06.

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Comparing Decimals: To compare two decimals, first compare the whole number part. If they are equal, compare the tenths place, then the hundredths place. For example, 0.50.5 is greater than 0.050.05 because 55 tenths is more than 00 tenths.

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Decimals on a Number Line: A number line between two whole numbers (like 00 and 11) can be divided into 10 equal parts to show tenths. Each mark represents 0.1,0.2,0.30.1, 0.2, 0.3, and so on. The midpoint between 0.20.2 and 0.30.3 would be 0.250.25 (hundredths).

📐Formulae

Decimal Value=NumeratorPower of 10\text{Decimal Value} = \frac{\text{Numerator}}{\text{Power of 10}}

Expanded Form:a.bc=a+b10+c100\text{Expanded Form}: a.bc = a + \frac{b}{10} + \frac{c}{100}

1 mm=110 cm=0.1 cm1 \text{ mm} = \frac{1}{10} \text{ cm} = 0.1 \text{ cm}

1 Paisa=Rs. 1100=Rs. 0.011 \text{ Paisa} = \text{Rs. } \frac{1}{100} = \text{Rs. } 0.01

1 cm=1100 m=0.01 m1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}

💡Examples

Problem 1:

Convert the fraction 75100\frac{75}{100} into a decimal and write its expanded form.

Solution:

Step 1: To convert 75100\frac{75}{100} to a decimal, we see there are two zeros in the denominator, so we place the decimal point two places from the right. 75100=0.75\frac{75}{100} = 0.75. \ Step 2: Expanded form using fractions: 0+710+51000 + \frac{7}{10} + \frac{5}{100}. \ Step 3: Expanded form using decimals: 0+0.7+0.050 + 0.7 + 0.05.

Explanation:

We identify the place value of each digit. The 77 is in the tenths place and 55 is in the hundredths place.

Problem 2:

Rohan has a pencil of length 88 cm and 66 mm. Express the length of the pencil in centimeters using decimals.

Solution:

Step 1: We know that 10 mm=1 cm10 \text{ mm} = 1 \text{ cm}. \ Step 2: Therefore, 1 mm=110 cm=0.1 cm1 \text{ mm} = \frac{1}{10} \text{ cm} = 0.1 \text{ cm}. \ Step 3: Convert 6 mm6 \text{ mm} to cm: 6×0.1 cm=0.6 cm6 \times 0.1 \text{ cm} = 0.6 \text{ cm}. \ Step 4: Add the whole cm part to the decimal part: 8 cm+0.6 cm=8.6 cm8 \text{ cm} + 0.6 \text{ cm} = 8.6 \text{ cm}.

Explanation:

To convert mm to cm, we divide by 10 because there are 10 millimeters in every centimeter. This moves the value to the tenths place.