Question

STANDARD FORM MATHS HELP. POINTS

Answer 1

Just use Pythagoras theorem to find the shortest distance between the two planets, (as it is along its hypotenuse)

The distance QR is :

`\qquad \sf \rightarrow d = \sqrt{(1.6 * 10 {}^(7)) {}^(2) + (3.6 * 10 {}^(6) ) {}^(2) }`

`\qquad \sf \rightarrow d = \sqrt{2.56 * 10 {}^(14) + 12.96 * 10 {}^(12) {}^{} }`

`\qquad \sf \rightarrow d = \sqrt{256* 10 {}^(12) + 12.96 * 10 {}^(12) {}^{} }`

`\qquad \sf \rightarrow d = \sqrt{(256 + 12.96 )* 10 {}^(12) {}^{} }`

`\qquad \sf \rightarrow d = \sqrt{(268.96 )* 10 {}^(12) {}^{} }`

`\qquad \sf \rightarrow d = 16.4* 10 {}^(6) {}^{}`

Answer 2

• 1.64×10⁷ km
• 16,400,000 km ("standard form" in the US)

Explanation:

You want the length of the hypotenuse of a right triangle with sides given as 3.6×10⁶ km and 1.6×10⁷ km.

Pythagorean theorem

The Pythagorean theorem tells you the relationship between the side lengths and the hypotenuse of a right triangle:

c² = a² +b²

RQ² = PQ² +PR²

RQ = √((3.6×10⁶)² +(1.6×10⁷)²) = 1.64×10⁷ . . . . . use numbers, take the root

The distance between planets Q and R is 1.64×10⁷ km.

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Additional comment

The "standard form" of a number is different by location. In the US, it is written with the decimal point to the right of the units digit. In other places, "standard form" has the decimal point to the right of the most-significant digit, and a power of ten as a multiplier.

You may recognize the ratio of the given numbers is 9:40, telling you these lengths are a multiple of the {9, 40, 41} Pythagorean triple. That is, the distance RQ is 41/40 times the distance RP.

Any spreadsheet or scientific or graphing calculator can do the necessary arithmetic using the numbers in "scientific notation" format. Spreadsheets, in particular, use E() to signify ×10^(). That is, 3.6×10⁶ is entered into a spreadsheet as 3.6E6. The attached calculator display shows it can use the same sort of format.