Simplify: 10^−3 (1 point)

Question

1/10^−3
1/−10^3
1/10^3
−10^3

Answer 1

1/10^3

Answer 2

A rectangle has length 9.3×10^2 cm and width 8.1×10 cm. Which of these statements are true?(4 points)
True or False
The area of the rectangle is 7.533×10^4 cm^2
The perimeter of the rectangle is 1.71×10^3 cm
The length of the rectangle is approximately 1.15×10 times greater than the width
The length of the rectangle squared is approximately 8.65×10^5

Answer 3

Let's solve each statement one by one:

1. The area of the rectangle is the length multiplied by the width:
Area = (9.3×10^2 cm)(8.1×10 cm) = 75.33×10^4 cm^2 = 7.533×10^5 cm^2
So, the statement "The area of the rectangle is 7.533×10^4 cm^2" is False.

2. The perimeter of a rectangle is given by:
Perimeter = 2(length + width) = 2(9.3×10^2 cm + 8.1×10 cm) = 2(9.3×10^2 cm + 8.1×10 cm) = 2(17.4×10^2 cm) = 34.8×10^2 cm = 3.48×10^3 cm
The statement "The perimeter of the rectangle is 1.71×10^3 cm" is False.

3. The length of the rectangle is approximately 1.15×10 times greater than the width:
Length = 9.3×10^2 cm
Width = 8.1×10 cm
Ratio of length to width: 9.3×10^2 / 8.1×10 = 9.3 / 8.1 = 1.148... ≈ 1.15 (rounded to two decimal places)
The statement "The length of the rectangle is approximately 1.15×10 times greater than the width" is True.

4. The length of the rectangle squared is approximately 8.65×10^5:
Length squared = (9.3×10^2 cm)^2 = 9.3^2 × 10^4 cm^2 = 86.49×10^4 cm^2 = 8.649×10^5 cm^2
The statement "The length of the rectangle squared is approximately 8.65×10^5" is True.

Answer 4

A city has two water towers. One tower holds 7.35×10^5 gallons of water. The other holds 9.78×10^5 gallons of water. What is the combined water capacity in Scientific Notation?(1 point)
7.1883×10^11
1.713×10^6
2.43×10^5
7.1883×10^26

Answer 5

To find the combined water capacity, we simply add the amounts of water in each tower:

(7.35×10^5 gallons) + (9.78×10^5 gallons) = 7.35×10^5 gallons + 9.78×10^5 gallons = 17.13×10^5 gallons

Now, we express 17.13×10^5 in scientific notation by converting it to a single digit before the decimal point:

17.13×10^5 = 1.713×10^(5+1) = 1.713×10^6

Therefore, the combined water capacity in scientific notation is 1.713×10^6 gallons.

Answer 6

Which of these is correct?(1 point)
(8.8×10^8)(4.2×10^7)=13×10^15
(9.9×10^7)(5.8×10^6)=5.72×10^13
(4.6×10^5)(2.1×10^4)=2.5×10
(2.9×10^8)(1.3×10^7)=3.77×10^15

Answer 7

Let's calculate each of these multiplications:

1. (8.8×10^8)(4.2×10^7) = 8.8 * 4.2 * 10^(8+7) = 36.96 * 10^15 = 3.696×10^16

2. (9.9×10^7)(5.8×10^6) = 9.9 * 5.8 * 10^(7+6) = 57.42 * 10^13 = 5.742×10^14

3. (4.6×10^5)(2.1×10^4) = 4.6 * 2.1 * 10^(5+4) = 9.66 * 10^9 = 9.66×10^9

4. (2.9×10^8)(1.3×10^7) = 2.9 * 1.3 * 10^(8+7) = 3.77 * 10^15 = 3.77×10^15

Therefore, the correct statement is:
(2.9×10^8)(1.3×10^7) = 3.77×10^15.

Answer 8

How many times larger is 9×10^−8 than 3×10^−12 ?(1 point)
6×10^−4
3×10^4
3×10^3
6×10^−3

Answer 9

To find how many times larger 9×10^-8 is than 3×10^-12, we divide the larger value by the smaller value:

(9×10^-8) / (3×10^-12) = (9 / 3) * (10^-8 / 10^-12)
= 3 * 10^( -8 - ( -12 ) )
= 3 * 10^-8+12
= 3 * 10^4
= 3×10^4

Therefore, 9×10^-8 is 3×10^4 times larger than 3×10^-12.

Answer 10

Divide 6.1×10^20 by 3.2×10^5 . Express your answer in Scientific Notation.(6 points)
Step 1: ? Result: ?
Step 2: ? Result: ?
Step 3: ?
Final answer: ?
Step 1 and results:
Add coefficients
Subtract coefficients
Divide coefficients
2.9
1.91
9.3
Step 2 and results:
10^25
10^15
10^4
Divide exponents
Subtract exponents
Add exponents
Step 3 and results:
Make sure your answer is in scientific notation
1.91 x 10^15
2.9 x 10^25
9.3 x 10^4

Answer 11

Step 1:
Divide coefficients: 6.1 / 3.2 = 1.90625 ≈ 1.91
Subtract exponents: 20 - 5 = 15

Step 2:
Final answer: 1.91 x 10^15

Therefore, when dividing 6.1×10^20 by 3.2×10^5, the final answer in scientific notation is 1.91 x 10^15.