Roughly, it takes light less than 0.000000003 of a second to travel a one-meter distance. Express this number in the form of a × 10^n where 1 < a < 10 and is a one-digit number.
To express the given number in scientific notation, we need to move the decimal point eight places to the left. Since every place we move the decimal point to the left decreases the value of the number by a factor of 10, we can write this as 3 × 10^(-9). In this form, 3 is between 1 and 10, and -9 is a one-digit number.
A wasp’s stinger has an average length of 2.67×10^−3 meter long. What is this length in decimal notation?
To convert the given number in scientific notation to decimal notation, we need to move the decimal point to the right three places. Since every place we move the decimal point to the right increases the value of the number by a factor of 10, we can write this as 0.00267.
5. Kendra finds the dimensions of a sticky note. She uses a meter stick to determine that the dimensions are 1.25×10^−8 meters wide by 2.5×10^−6 meters long. Use scientific notation to write the dimensions in millimeters.
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1 point
1.25×10^ −10 by 2.5×10^−8 millimeters
1.25×10^−11 by 2.5×10^−9 millimeters
1.25×10^−6 by 2.5×10^−4 millimeters
1.25×10^−5 by 2.5×10^−3 millimeters
To convert the dimensions from meters to millimeters, we need to multiply each dimension by 1000.
For the width: 1.25 × 10^(-8) meters × 1000 = 1.25 × 10^(-8) × 10^3 = 1.25 × 10^(-8+3) = 1.25 × 10^(-5) millimeters.
For the length: 2.5 × 10^(-6) meters × 1000 = 2.5 × 10^(-6) × 10^3 = 2.5 × 10^(-6+3) = 2.5 × 10^(-3) millimeters.
Therefore, the dimensions in millimeters are 1.25 × 10^(-5) by 2.5 × 10^(-3) millimeters.
So, the correct answer is 1.25 × 10^(-5) by 2.5 × 10^(-3) millimeters.
6. In government class, Nadia computed the amount of debt of the federal government after a third of it was paid in 1995. The calculator displayed the number 3.28E12. What is this number in scientific notation?
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1 point
3.28 x 10^-12
3.28×10^12
12 x 10^3.28
3.28 x 12 ^10
The number 3.28E12 is already in scientific notation. In scientific notation, the "E" represents "x 10^", so 3.28E12 means 3.28 x 10^12.
Therefore, the number 3.28E12 in scientific notation is 3.28 x 10^12.
7. Subtract 4.66×10^−5 − 7.34×10^−7
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1 point
-4.5866 x 10 ^-5
2.68 x 10^2
4.5866 x 10 ^ -5
-2/68 x 10^2
To subtract scientific notation, we need to ensure that the exponents are the same. In this case, we can rewrite the numbers as:
4.66 × 10^(-5) - 0.734 × 10^(-6)
Since the exponents are already the same, we can directly subtract the coefficients:
4.66 - 0.734 = 3.926
Therefore, the result of the subtraction is:
3.926 × 10^(-5)
So, the correct answer is 3.926 × 10^(-5).
Subtract 4.66×10^−5 − 7.34×10^−7
-4.5866 x 10 ^-5
2.68 x 10^2
4.5866 x 10 ^ -5
-2/68 x 10^2