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A field of 3.9 mi^2 is being subdivided into 1.3×10^3 family gardens. How many square miles will there be in each garden? Write the answer in scientific notation

User Icon for Bot GPT 3.5 Bot GPT 3.5 answered
1 year ago

To find the number of square miles in each garden, we need to divide the total area of the field by the number of gardens.

Area of the field = 3.9 mi^2
Number of gardens = 1.3 × 10^3

To divide the area by the number of gardens, we divide the values of the exponents:

3.9 ÷ 1.3 = 3
10^3 ÷ 10^3 = 0

Therefore, each garden will have an area of 3.0 × 10^0 square miles.

In scientific notation, 3.0 × 10^0 can be written as 3.0 square miles.

User Icon for Step-by-Step Bot Step-by-Step Bot answered
1 year ago

To find the square miles in each garden, we need to divide the total area of the field (3.9 mi^2) by the number of gardens (1.3×10^3).

First, perform the division:
3.9 mi^2 / 1.3×10^3 = 3.9 / 1.3 × 10^3 = 3 × 10^0 / 1.3 × 10^3

To divide numbers in scientific notation, subtract the exponent of the denominator from the exponent of the numerator, then divide the coefficient (number before the "x") of the numerator by the coefficient of the denominator.

3 × 10^0 / 1.3 × 10^3 = 3 / 1.3 × 10^(0-3) = 2.30769230769 × 10^(-3)

Therefore, there will be approximately 2.30769230769 × 10^(-3) square miles in each garden.

User Icon for Explain Bot Explain Bot answered
1 year ago

To find the number of square miles in each garden, we need to divide the total area of the field (3.9 mi^2) by the number of gardens (1.3×10^3).

To divide a number in scientific notation, we divide the coefficients and subtract the exponents.

So, 3.9 mi^2 ÷ (1.3×10^3) = 3.9 ÷ 1.3 × (10^2 ÷ 10^3)

Simplifying further, we get: 3.9 ÷ 1.3 × 10^(2-3)

Dividing the coefficients, we have: 3 ÷ 1 × 10^(2-3)

The exponent becomes negative since we are dividing by a larger number. Therefore, 10^(2-3) = 10^-1, which is equal to 0.1.

So, 3 ÷ 1 × 0.1 = 0.3

Therefore, there will be 0.3 square miles in each garden.

In scientific notation, this is written as: 3.0 x 10^-1 mi^2.