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A Peek Beyond the Point - The Need for Smaller Units

Grade 7CBSE

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

🔑Concepts

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Decimal numbers are an extension of the place value system used to represent parts of a whole. The decimal point separates the whole number part (on the left) from the fractional part (on the right).

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The 'Tenths' place represents 110\frac{1}{10} or 0.10.1. It is the first position to the right of the decimal point.

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The 'Hundredths' place represents 1100\frac{1}{100} or 0.010.01. It is the second position to the right of the decimal point.

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The 'Thousandths' place represents 11000\frac{1}{1000} or 0.0010.001. It is the third position to the right of the decimal point.

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Like Decimals: Decimals having the same number of decimal places are called like decimals (e.g., 1.451.45 and 23.0723.07).

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Unlike Decimals: Decimals having different numbers of decimal places are called unlike decimals (e.g., 2.52.5 and 2.582.58). They can be made 'like' by adding trailing zeros (e.g., 2.502.50 and 2.582.58).

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To compare decimals, first compare the whole number part. If they are equal, compare the tenths, then hundredths, and so on.

📐Formulae

1 Tenth=110=0.11 \text{ Tenth} = \frac{1}{10} = 0.1

1 Hundredth=1100=0.011 \text{ Hundredth} = \frac{1}{100} = 0.01

1 Thousandth=11000=0.0011 \text{ Thousandth} = \frac{1}{1000} = 0.001

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

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

1 g=11000 kg=0.001 kg1 \text{ g} = \frac{1}{1000} \text{ kg} = 0.001 \text{ kg}

💡Examples

Problem 1:

Write the following as decimals: 200+40+5+210+9100200 + 40 + 5 + \frac{2}{10} + \frac{9}{100}.

Solution:

245+0.2+0.09=245.29245 + 0.2 + 0.09 = 245.29

Explanation:

The whole number part is 200+40+5=245200 + 40 + 5 = 245. The decimal part has 22 in the tenths place and 99 in the hundredths place.

Problem 2:

Subtract 1.851.85 from 5.465.46.

Solution:

5.46−1.853.61\begin{array}{r} 5.46 \\ - 1.85 \\ \hline 3.61 \end{array}

Explanation:

Align the decimal points and digits according to their place value. Subtract starting from the rightmost digit, regrouping (borrowing) as necessary.

Problem 3:

Express 7575 paise as rupees using decimals.

Solution:

75 paise=₹75100=₹0.7575 \text{ paise} = ₹ \frac{75}{100} = ₹ 0.75

Explanation:

Since 100100 paise equals 11 Rupee, 11 paisa equals 1100\frac{1}{100} of a rupee. To convert paise to rupees, we divide by 100100.

Problem 4:

Add 0.007+8.5+30.080.007 + 8.5 + 30.08.

Solution:

0.00708.500+30.08038.587\begin{array}{r} 0.007 \\ 08.500 \\ + 30.080 \\ \hline 38.587 \end{array}

Explanation:

Convert all numbers to like decimals by adding trailing zeros so they all have three decimal places. Align the points and add.