Question

Expand 1965.245 using exponents

Answer 1

Answer:

answer for the given problem is given

Answer 2

Answer:

The expanded form of the number 1965.245 using exponents

= 10³ + 9×10² + 6×10¹ + 5×10⁰ + 2×10⁻¹ + 4×10⁻² + 5×10⁻³

Step-by-step explanation:

Given number is 1965.245

Required to expand the number 1965.245 using exponents

Expanding a number is the method of writing the number as the sum of the place values of all the digits of that number.

Recall the rules of exponents

a⁻ⁿ = $\frac{1}{a^n}$

a⁰ = 1

1965.245 can be written in expanded form as

1965.245 = 1000 + 900 + 60 + 5 + 0.2 + 0.04 + 0.005

= 1000 + 900 + 60 + 5 + $\frac{2}{10}$ + $\frac{4}{100}$ + $\frac{5}{1000}$

= 1×1000 + 9×100 + 6×10 + 5×1 + $\frac{2}{10^1}$ + $\frac{4}{10^2}$ + $\frac{5}{10^3}$

= 10³ + 9×10² + 6×10¹ + 5×10⁰ + 2×10⁻¹ + 4×10⁻² + 5×10⁻³

The expanded form of the number 1965.245 using exponents

= 10³ + 9×10² + 6×10¹ + 5×10⁰ + 2×10⁻¹ + 4×10⁻² + 5×10⁻³

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