CBSE Class 7 Maths: Fractions and Decimals Ex 2.5

Understanding How to Compare Decimals

To compare decimal numbers, it's like lining up two numbers to see which is truly greater or smaller. The trick is to look at their place values systematically. First, always compare the whole number part (the digits before the decimal point). If one decimal has a larger whole number part, then that decimal is definitively greater. For example, 7.5 is greater than 6.9 because 7 is greater than 6. If the whole number parts are the same, then you move to the tenths place (the first digit immediately after the decimal point). Compare these digits. The one with the larger digit in the tenths place is greater. If the tenths digits are also the same, you then move to the hundredths place, and then to the thousandths place, and so on, until you find a pair of digits that are different. A super helpful tip is to add zeros to the end of a decimal number so that both numbers have the same number of decimal places. This doesn't change the value but makes comparison visually clearer and easier, for instance, 0.5 can be seen as 0.50 when comparing it with 0.45 or 0.52. This systematic, place-value-focused approach ensures you always pick the correct larger or smaller decimal number confidently.

Step-by-Step Guide to Comparing Decimal Numbers

1. Step 1: Compare the Whole Number Parts — Look at the digits to the left of the decimal point. The number with the larger whole number part is the greater decimal. For example, to compare 12.34 and 9.87, since 12 is greater than 9, then 12.34 > 9.87.
2. Step 2: If Whole Number Parts are Equal, Compare the Tenths Digits — If the whole number parts are the same, move to the first digit immediately after the decimal point (the tenths place). The number with the larger tenths digit is greater. For example, to compare 5.62 and 5.39, the whole parts (5) are equal. Comparing the tenths digits, 6 is greater than 3, so 5.62 > 5.39.
3. Step 3: If Tenths Digits are Equal, Compare the Hundredths Digits — If both the whole number parts and the tenths digits are the same, move to the second digit after the decimal point (the hundredths place). The number with the larger hundredths digit is greater. For example, to compare 0.45 and 0.42, the whole parts (0) and tenths (4) are equal. Comparing the hundredths digits, 5 is greater than 2, so 0.45 > 0.42.
4. Step 4: Continue Comparing Digits Place by Place — If necessary, continue this process for the thousandths, ten-thousandths, and so on, until you find a place where the digits are different. Remember, you can add zeros at the end of a decimal number without changing its value to make the number of decimal places equal, which often helps in visual comparison. For example, to compare 3.7 and 3.705. You can write 3.7 as 3.700. Comparing 3.700 and 3.705, the whole parts (3), tenths (7), and hundredths (0) are equal. In the thousandths place, 0 is less than 5, so 3.700 < 3.705, which means 3.7 < 3.705.

Converting Units Using Decimals (Money, Length, Weight)

Decimals are incredibly useful for expressing quantities in different units, especially when dealing with money, length, or weight, allowing for greater precision. The key is to remember the specific conversion factor between the units and understand how to properly divide or multiply by powers of 10 (10, 100, 1000). When converting a smaller unit to a larger unit, you generally need to divide by the appropriate conversion factor. For instance, there are 100 paise in 1 rupee, so to convert a value given in paise to rupees, you divide the number of paise by 100. This action shifts the decimal point two places to the left. Similarly, 100 centimetres make 1 metre, and 1000 metres make 1 kilometre. Therefore, converting a measurement from centimetres to metres involves dividing by 100, and converting metres to kilometres requires dividing by 1000. For weights, 1000 grams make 1 kilogram, so converting a mass from grams to kilograms involves dividing by 1000. In essence, dividing by 10, 100, or 1000 simply means shifting the decimal point to the left by 1, 2, or 3 places, respectively. This straightforward method makes all kinds of unit conversions using decimal numbers precise and easy to manage.

YoLearn AI Tutor's Exam Tips: Avoid These Common Mistakes!

To ace your exams, be mindful of these frequent errors students make with decimals:

• Ignoring Whole Number Parts First: Always start by comparing the digits before the decimal point. Many students mistakenly think 1.99 is larger than 2.01 because '99' seems bigger than '01'. Remember, 2.01 has a larger whole number (2) than 1.99 (1).
• Misinterpreting Number of Digits After Decimal: Don't assume that a decimal with more digits is automatically larger. For example, 0.5 is actually larger than 0.125. It helps to think of 0.5 as 0.500 for comparison.
• Incorrect Decimal Point Placement During Unit Conversion: When dividing by 10, 100, or 1000 to convert smaller units to larger ones, remember to move the decimal point to the left by the number of zeros. For example, 50 cm is 0.50 m (not 5.0 m).
• Forgetting Conversion Factors: Make sure to memorise or have handy the standard conversion factors: 1 Rupee = 100 Paise, 1 m = 100 cm, 1 km = 1000 m, 1 kg = 1000 g. Writing them down during practice can prevent errors.

Practice Questions with Solutions

• Q: Which is greater: 2.03 or 2.30?
• A: Step 1: Compare the whole number parts. Both numbers have '2' as the whole number part, which is equal. Step 2: Compare the tenths digits. For 2.03, the tenths digit is '0'. For 2.30, the tenths digit is '3'. Step 3: Since 3 > 0, the number with '3' in the tenths place is greater. Final answer: 2.30 is greater than 2.03.
• Q: Express 7 rupees 7 paise as rupees using decimals.
• A: Step 1: Identify the conversion factor. We know that 1 Rupee = 100 Paise. Step 2: Convert the 'paise' part to rupees by dividing by 100. 7 paise = 7 / 100 rupees = 0.07 rupees. Step 3: Add this decimal part to the whole rupees. Final answer: 7 rupees + 0.07 rupees = 7.07 rupees.
• Q: Express 35 mm in cm, m and km.
• A: Step 1: Convert mm to cm. (1 cm = 10 mm). So, 35 mm = 35 / 10 cm = 3.5 cm. Step 2: Convert cm to m. (1 m = 100 cm). So, 3.5 cm = 3.5 / 100 m = 0.035 m. Step 3: Convert m to km. (1 km = 1000 m). So, 0.035 m = 0.035 / 1000 km = 0.000035 km. Final answer: 35 mm = 3.5 cm = 0.035 m = 0.000035 km.
• Q: Arrange the following decimals in ascending order: 0.5, 0.05, 0.505, 0.55
• A: Step 1: Make all decimals have the same number of decimal places by adding trailing zeros. The maximum number of decimal places is 3 (in 0.505). 0.5 becomes 0.500 0.05 becomes 0.050 0.505 remains 0.505 0.55 becomes 0.550 Step 2: Compare the numbers place by place, starting from the whole number part (all are 0). Step 3: Compare the tenths digits: 0.050 (0), 0.500 (5), 0.505 (5), 0.550 (5). The smallest is 0.050. Step 4: Among the remaining (0.500, 0.505, 0.550), compare the hundredths digits: 0.500 (0), 0.505 (0), 0.550 (5). The next smallest are 0.500 and 0.505. Between these two, compare thousandths: 0.500 (0) and 0.505 (5). So, 0.500 is smaller than 0.505. Step 5: The largest is 0.550. Final answer: 0.05, 0.5, 0.505, 0.55

Frequently Asked Questions