329.25 = 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻². State whether the statement is true or false.

Solution:

Given, 329.25 = 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻².

RHS: 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻²

3 × 10² = 300

2 × 10¹ = 20

Using law of exponents,

a° = 1, where a ≠ 0

9 × 10⁰ = 9

Using law of exponents,

a⁻ⁿ = 1/aⁿ

2 × 10⁻¹ = 2/10 = 0.2

5 × 10⁻² = 5/100 = 0.05

Now, 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻² = 300 + 20 + 9 + 0.2 + 0.05

= 329 + 0.25

= 329.25

LHS = RHS

Therefore, 3 × 10² + 2 × 10¹ + 9 × 100 + 2 × 10⁻¹ + 5 × 10⁻² = 329.25.

✦ Try This: 738.26 = 7 × 10² + 3 × 10¹ + 8 × 10⁰ + 2 × 10⁻¹ + 6 × 10⁻². State whether the statement is true or false.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 12

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NCERT Exemplar Class 8 Maths Chapter 8 Problem 70

329.25 = 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻². State whether the statement is true or false.

Summary:

The given statement, ”329.25 = 3 × 10² + 2 × 10¹ + 9 × 10⁰ + 2 × 10⁻¹ + 5 × 10⁻²” is true.

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