Mars 141,000,000 miles, and Jupiter 480,000,000 miles Which expression represent in scientific notation the distance Mercury is from the Sun? Answers A) 0.36 x 10 to the 8 power
B) 3.6 x 10 to the 6 power C) 3.6 x 10 to the 7 power D) 36 x 10 to the 6 power
B) 3.6 x 10 to the 6 power C) 3.6 x 10 to the 7 power D) 36 x 10 to the 6 power
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You preform a version of this every day without even thinking about it. As I saw the number 36,000,000, I read "thirty-six million. I instantly broke the number into factors.
It can be further factored to our benefit. Million is equal to
10 x 100,000 =
10 x 10 x 10,000 =
10 x 10 x 10 x 1,000 =
10 x 10x x 10 x 10 x 100 =
10 x10 x 10 x 10 x 10 x 10.
Six tens; which can be more easily written 10⁶: 10 to the power of 6.
But 36 can be rewritten 3.6 x 10. And that 10 can be added to the other six giving 10⁷. (Notice that I multiplied by adding. One of the many benefits of scientific notation.)
3.6 x 10⁷ is the proper form for scientific notation, with one digit ahead of the decimal place and any number of digits behind the decimal place as required by the desired accuracy.
A, C and D are of equal value, but only C is scientific notation.
D is in engineering notation: up to three digits before the decimal place and a power that is a multiple of three: -3 (milli), -6 (micro), -9 (nano), 0 (base), 3 (kilo), 6 (mega), 9 (giga), 12 (tera), and so on, and any number of digits behind the decimal place as required by the desired accuracy.
B is not equal to thirty-six million.
It can be further factored to our benefit. Million is equal to
10 x 100,000 =
10 x 10 x 10,000 =
10 x 10 x 10 x 1,000 =
10 x 10x x 10 x 10 x 100 =
10 x10 x 10 x 10 x 10 x 10.
Six tens; which can be more easily written 10⁶: 10 to the power of 6.
But 36 can be rewritten 3.6 x 10. And that 10 can be added to the other six giving 10⁷. (Notice that I multiplied by adding. One of the many benefits of scientific notation.)
3.6 x 10⁷ is the proper form for scientific notation, with one digit ahead of the decimal place and any number of digits behind the decimal place as required by the desired accuracy.
A, C and D are of equal value, but only C is scientific notation.
D is in engineering notation: up to three digits before the decimal place and a power that is a multiple of three: -3 (milli), -6 (micro), -9 (nano), 0 (base), 3 (kilo), 6 (mega), 9 (giga), 12 (tera), and so on, and any number of digits behind the decimal place as required by the desired accuracy.
B is not equal to thirty-six million.
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36,000,000 mile can be expressed in scientific notation by simply counting from the last zero to the last digit of the decimal point. Use this counts for the value of the exponent. So all this numbers are equivalent.
36.0 *10^6
3.6*10^7
0.36*10^8
So B) is incorrect. A), C) & D) are all correct equivalent notations.
36.0 *10^6
3.6*10^7
0.36*10^8
So B) is incorrect. A), C) & D) are all correct equivalent notations.
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Count the digits to the right of the decimal - that's the "power".