krit.club logo

A Peek Beyond the Point - A Hundredth Part

Grade 7CBSE

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

🔑Concepts

•

A hundredth part is one of a hundred equal parts of a whole. In decimal notation, it is written as 0.010.01, and as a fraction, it is 1100\frac{1}{100}.

•

In the place value system, the first place to the right of the decimal point is the 'tenths' (110\frac{1}{10}) and the second place is the 'hundredths' (1100\frac{1}{100}).

•

A decimal number like 14.2514.25 can be expanded as 10+4+210+510010 + 4 + \frac{2}{10} + \frac{5}{100}.

•

To convert a fraction with denominator 100100 into a decimal, we count two places from the right of the numerator and place the decimal point. For example, 45100=0.45\frac{45}{100} = 0.45 and 7100=0.07\frac{7}{100} = 0.07.

•

Decimals are compared by first looking at the whole number part, then the tenths place, and then the hundredths place. For example, 0.5>0.480.5 > 0.48 because 55 tenths is greater than 44 tenths.

•

When adding or subtracting decimals, align the decimal points vertically. If the number of decimal places is different, add trailing zeros to make them 'like decimals'.

📐Formulae

Value of Hundredth Place=0.01=1100\text{Value of Hundredth Place} = 0.01 = \frac{1}{100}

Expanded Form: xy.ab=(x×10)+(y×1)+(a×110)+(b×1100)\text{Expanded Form: } xy.ab = (x \times 10) + (y \times 1) + \left(a \times \frac{1}{10}\right) + \left(b \times \frac{1}{100}\right)

Rupees to Paise: ₹1=100 paise  ⟹  1 paisa=₹1100=₹0.01\text{Rupees to Paise: } ₹ 1 = 100 \text{ paise} \implies 1 \text{ paisa} = ₹ \frac{1}{100} = ₹ 0.01

Metres to Centimetres: 1 m=100 cm  ⟹  1 cm=1100 m=0.01 m\text{Metres to Centimetres: } 1 \text{ m} = 100 \text{ cm} \implies 1 \text{ cm} = \frac{1}{100} \text{ m} = 0.01 \text{ m}

💡Examples

Problem 1:

Convert the fraction 531005 \frac{3}{100} into a decimal.

Solution:

5.035.03

Explanation:

The whole number part is 55. The fraction 3100\frac{3}{100} represents 33 hundredths. Since there are no tenths, we place a 00 in the tenths place and 33 in the hundredths place, resulting in 5.035.03.

Problem 2:

Add 12.7512.75 and 4.84.8.

Solution:

12.75+04.8017.55\begin{array}{r} 12.75 \\ + 04.80 \\ \hline 17.55 \end{array}

Explanation:

We align the decimal points and add a zero to 4.84.8 to make it 4.804.80 (making them like decimals). Then we perform vertical addition: 5+0=55+0=5, 7+8=157+8=15 (carry 1), 2+4+1=72+4+1=7, and 1+0=11+0=1.

Problem 3:

Subtract 2.452.45 from 10.0010.00.

Solution:

10.00−02.4507.55\begin{array}{r} 10.00 \\ - 02.45 \\ \hline 07.55 \end{array}

Explanation:

Aligning the decimal points, we subtract 2.452.45 from 10.0010.00 using the standard borrowing method. 10.00−2.45=7.5510.00 - 2.45 = 7.55.

Problem 4:

Express 8585 paise as Rupees using decimals.

Solution:

₹0.85₹ 0.85

Explanation:

Since 100100 paise = ₹1₹ 1, then 8585 paise = ₹85100₹ \frac{85}{100}. Dividing by 100100 moves the decimal point two places to the left, giving ₹0.85₹ 0.85.