NCERT Class 7 Maths Chapter 12
Another Peek Beyond the Point
This chapter from Ganita Prakash Part 2 extends CBSE Class 7 students' knowledge of decimals to include multiplication and division of decimals by decimals, and conversion between fractions and decimals including repeating decimals. Students also explore percentages as a special form of decimal and fraction, and apply these skills in contexts such as discounts, profit and loss, and data representation.
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Key Terms
- Repeating Decimal
- A decimal in which one or more digits repeat endlessly after the decimal point. For example, 1/3 = 0.333… and 1/6 = 0.1666… A bar is placed over the repeating digit(s).
- Terminating Decimal
- A decimal that has a finite number of digits after the decimal point. For example, 1/4 = 0.25 and 3/8 = 0.375.
- Percentage
- A fraction with denominator 100, expressed using the % symbol. For example, 45% means 45/100 or 0.45.
- Profit and Loss
- If selling price > cost price, there is a profit; if selling price < cost price, there is a loss. Profit/loss percentage is calculated on the cost price.
- Discount
- A reduction in the marked price of an article. Discount = Marked Price – Selling Price. Discount percentage is calculated on the marked price.
- Rational Number
- A number that can be expressed as a fraction p/q where p and q are integers and q ≠ 0. All terminating and repeating decimals are rational numbers.
Frequently Asked Questions
What is the difference between a terminating and a repeating decimal?▾
A terminating decimal ends after a fixed number of digits (e.g., 0.25, 0.375). A repeating (or recurring) decimal has one or more digits that repeat infinitely (e.g., 0.333… = 0.3̄, 0.142857142857… = 0.1̄4̄2̄8̄5̄7̄). All fractions produce either terminating or repeating decimals.
How do you convert a percentage to a decimal and a fraction?▾
To convert a percentage to a decimal, divide by 100. For example, 35% = 35/100 = 0.35. To convert to a fraction, write it as a fraction over 100 and simplify: 35% = 35/100 = 7/20.
How do you calculate profit or loss percentage?▾
Profit % = (Profit / Cost Price) × 100, and Loss % = (Loss / Cost Price) × 100. For example, if CP = ₹200 and SP = ₹240, Profit = ₹40, so Profit % = (40/200) × 100 = 20%.
How do you multiply a decimal by a decimal?▾
Multiply the numbers as if they were whole numbers, then count the total decimal places in both numbers and place the decimal point that many places from the right in the product. For example, 2.3 × 1.4: 23 × 14 = 322, total decimal places = 2, so the answer is 3.22.
What is the formula for calculating discount percentage?▾
Discount % = (Discount / Marked Price) × 100. For example, if the marked price is ₹500 and the discount is ₹75, then Discount % = (75/500) × 100 = 15%.
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