# Question d6a70

Jul 24, 2014

Sorry, I can't find any suitable YouTube videos of the type you want, nor have I the skills or equipment to mane a good video.

First, you must know the SI multiplying prefixes.

For example, milli- means "× ¹/₁₀₀₀" and kilo- means "× 1000".

The symbol for milli- is "m"; the symbol for kilo- is "k"; and the symbol for metre is "m".

Thus, 1 mm = ¹/₁₀₀₀ m and 1000 mm = 1 m.
Also, 1 km = 1000 m

Second, you must know how to convert these relationships into conversion factors.

Since 1000 mm = 1 m, (1000"mm")/(1"m")" = 1, and $\left(1 \text{m")/(1000"mm}\right)$ = 1

Since 1 km = 1000 m, $\left(1 \text{km")/(1000"m}\right)$ = 1, and (1000"m")/(1"km")"# = 1

All four of the above fractions equal 1. We can multiply them by other measurements to change the units. We choose the one that gives us the desired units in the answer.

For example to change 2 mm to metres, we write

2 mm × $\left(1 \text{m")/(1000"mm}\right)$ = 0.002 m

We chose the conversion factor that had "mm"" on the denominator. This made the "mm" cancel, so the answer had the units of "m".

How do we convert 7500 × 10⁻¹⁴ mm to metres? For this, we must use a scientific calculator.

The calculator must be able to handle scientific notation.

Third, you must know how to enter scientific notation into the calculator. Every model is different.

Most scientific calculators express numbers like 2×10⁻³ as 2E-3.

The "E" stands for "Exponent" or "×10 to the…"

Here's how to enter 7500 × 10⁻¹⁴.

1. Enter 1700
2. Press "EXP" or "EE" or "2nd EE" (depending on your calculator).
3. Press the "Change Sign" key: "(-)" or "+/-" (depending on your calculator).
4. Enter 14.

Always enter scientific notation in this way. Do not use the multiplication key "×" or the subtract key "-". That will get you into trouble in some calculations.

Fourth, you must know how to do the calculations.

In your problem, we must convert millimetres to metres and then convert metres into kilometres.

To convert 7500 × 10⁻¹⁴ mm to metres, we write

7500 × 10⁻¹⁴ mm × $\left(1 \text{m")/(1000"mm}\right)$ = ?

In the calculator, we enter 7500 × 10⁻¹⁴, press "÷", enter 1000, and press "=".

The calculator displays the answer as 7.5E-14. You write the answer as 7.5 × 10⁻¹⁴ m.

To convert this to kilometres, we write

7.5 × 10⁻¹⁴ m × $\left(1 \text{km")/(1000"m}\right)$ = ?

The calculator already displays the number 7.5E-14. We want to divide this by 1000.

Press "÷", enter 1000, and press "=".

The calculator displays the answer as 7.5E-17. You write the answer as 7.5 × 10⁻¹⁷ km.

Fifth, (optional) you should know how to do "string calculations". We could have written the problem as

7500 × 10⁻¹⁴ mm × $\left(1 \text{m")/(1000"mm") × (1"km")/(1000"m}\right)$.

To do the calculation all in one step, we would enter

7500E-14, ÷, 1000, ÷, 1000 =

We get the same answer as before.