A tape dispenser holds 1.14×10^4 mm of tape that is 12.7 mm wide. Multiply the two numbers to find the total area in square millimeters of tape. Write the product in scientific notation.
To find the total area in square millimeters of tape, we need to multiply the length and the width of the tape.
Length of tape = 1.14 x 10^4 mm
Width of tape = 12.7 mm
Total area = (1.14 x 10^4 mm) * (12.7 mm)
Total area = 1.448 x 10^5 mm^2
Therefore, the total area of the tape is 1.448 x 10^5 mm^2.
To find the total area in square millimeters of the tape, we need to multiply the length and the width of the tape.
The length of the tape, given as 1.14×10^4 mm, represents a number in scientific notation. In scientific notation, a number is represented as a product of a coefficient and a power of 10. In this case, the coefficient is 1.14 and the power of 10 is 4. To convert this to standard form, we need to multiply 1.14 by 10 raised to the power of 4.
1.14 × 10^4 = 1.14 × 10,000 = 11,400 mm
So, the length of the tape is 11,400 mm.
Now, we need to multiply the length (11,400 mm) by the width (12.7 mm) to find the total area:
11,400 mm × 12.7 mm = 144,780 mm^2
Therefore, the total area of the tape is 144,780 square millimeters.
To write the product in scientific notation, we need to express it as a coefficient multiplied by a power of 10. Since the coefficient is greater than or equal to 1 and less than 10, we can express it as 1.4478 multiplied by 10 raised to the power of 5 (since we moved the decimal point 5 places to the right).
So, the product of the length and width of the tape in scientific notation is:
1.4478 × 10^5 mm^2
To find the total area of the tape, we need to multiply the length of the tape by its width.
Length of the tape = 1.14 × 10^4 mm
Width of the tape = 12.7 mm
Total area = Length × Width = (1.14 × 10^4 mm) × (12.7 mm)
To multiply these numbers, we need to multiply the coefficients and add the exponents:
1.14 × 10^4 × 12.7
Multiplying the coefficients: 1.14 × 12.7 = 14.478
Adding the exponents: 10^4 × 10^0 = 10^4
Thus, the total area of the tape is 14.478 × 10^4 square millimeters, which can be written in scientific notation as 1.4478 × 10^5 square millimeters.