Chapter Overview
Decimals extend the place-value system to quantities smaller than one. They are especially useful in measurement, money and scientific data, where tenths and hundredths describe parts of a whole precisely.
This chapter belongs to Ganita Prakash, Grade 7. Focus on explaining each step, checking whether an answer is reasonable, and comparing more than one solution method.
Learning Objectives
After studying this chapter, you should be able to:
- explain and apply decimal place value;
- explain and apply fractions and decimals;
- explain and apply comparing decimals;
- explain and apply addition and subtraction;
- communicate the reasoning behind a solution clearly;
- check answers using estimation, substitution, or a second method.
Key Concepts
| Concept | Meaning | |---|---| | Decimal place value | The first digit after the decimal point represents tenths, the second hundredths and the third thousandths. | | Fractions and decimals | A fraction with denominator 10, 100 or 1000 can be written directly as a decimal. Equivalent fractions help convert other fractions. | | Comparing decimals | Align decimal points and add trailing zeros when useful. Compare whole-number parts first and then tenths, hundredths and later places. | | Addition and subtraction | Write decimal points in one vertical line so digits of equal place value are combined. |
Detailed Explanation
Decimal place value
The first digit after the decimal point represents tenths, the second hundredths and the third thousandths.
Fractions and decimals
A fraction with denominator 10, 100 or 1000 can be written directly as a decimal. Equivalent fractions help convert other fractions.
Comparing decimals
Align decimal points and add trailing zeros when useful. Compare whole-number parts first and then tenths, hundredths and later places.
Addition and subtraction
Write decimal points in one vertical line so digits of equal place value are combined.
Do not memorise a rule without testing it on examples. Ask what each number, operation, line, or symbol represents and whether the result fits the original situation.
Important Rules and Formulae
- Appending zeros to the right does not change a decimal:
3.5 = 3.50. - Never align decimals by their final digit; align the decimal points.
- Units must match before adding measurements.
Worked Examples
Example 1
Problem: Convert 37/100 and 2 4/10 to decimals.
Solution: 37/100 = 0.37; 2 4/10 = 2.4.
Example 2
Problem: A rope is 12.75 m long and 3.8 m is cut off. How much remains?
Solution: Write 3.8 as 3.80. Then 12.75 − 3.80 = 8.95 m.
Show the mathematical statement, substitution or construction step before writing the final answer. Include units wherever the quantity is measured.
Common Mistakes
- Thinking 0.8 is smaller than 0.75 because 8 is smaller than 75.
- Writing
2.4 + 0.36 = 2.40instead of 2.76. - Ignoring measurement units.
Quick Revision
- Decimal place value: The first digit after the decimal point represents tenths, the second hundredths and the third thousandths.
- Fractions and decimals: A fraction with denominator 10, 100 or 1000 can be written directly as a decimal.
- Comparing decimals: Align decimal points and add trailing zeros when useful.
- Addition and subtraction: Write decimal points in one vertical line so digits of equal place value are combined.
Practice Questions
- What is the place value of 7 in 4.072?
- Arrange 0.5, 0.05 and 0.505 in ascending order.
- Find
8.4 − 2.75. - Convert 625 paise to rupees.
Answers and Explanations
- Seven hundredths, or 0.07.
- 0.05, 0.5, 0.505.
- 5.65.
- ₹6.25.
Self-Check
Explain one rule from this chapter in your own words, create a fresh example, solve it, and verify the answer. If the explanation and verification agree, the concept is understood rather than merely memorised.