Question

Write the following in expanded form using exponents of 10.
a) 23.869
b) 9.586147
c) 35.861496
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Answer 1

Answer:

a)2×10^2 + 3×10^1 + 8×10^-1 + 6×10^-2 + 9×10^-3

b)9×10^1 + 5×10^-1 + 8×10^-2 + 6×10^-3 + 1×10^-4 + 4×10^-5 + 7×10^-6

c)3×10^2 + 5×10^1 + 8×10^-1 + 6×10^-2 + 1×10^-3 + 4×10^-4 + 9×10^-5 + 6×10^-6

Answer 2

→ The term "Exponents of 10" means a number in which the base is 10 while the exponent is an integer. For example 10², 10⁷, and 10⁻⁵.

→ We can break down a given number and express it in terms of exponents of 10. For different types of numbers, we use different exponents of 10.

→ A triple-digit number can be expressed using exponents of 10 with 10² being the greatest exponent of 10 used. Similarly, a double-digit number can be expressed using exponents of 10 with 10¹ being the greatest exponent of 10 used.

→ A decimal number can be expressed using exponents of 10 with negative exponents.

→ The following are the numbers in their expanded form using the exponents of 10:

(a) 23.869 = (2×10¹) + (3×10⁰) + (8×10⁻¹) + (6×10⁻²) + (9×10⁻³)

(b) 9.586147 = (9×10⁰) + (5×10⁻¹) + (8×10⁻²) + (6×10⁻³) + (1×10⁻⁴) + (4×10⁻⁵) + (7×10⁻⁶)

(c) 35.861496 = (3×10¹) + (5×10⁰) + (8×10⁻¹) + (6×10⁻²) + (1×10⁻³) + (4×10⁻⁴) + (9×10⁻⁵) + (6×10⁻⁶)

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