Question

12 écris les mesures suivantes en notation scientifique et dans les unités du si sans préfixe. ensuite, place - les en ordre croissant. a. 0,000 000 24 mm b. 20 nm c. 9,3×10¹m d. 2×10⁻⁶hm e. 40 000 000 000 cm f. 0,3 gm g. cent mille décimètres

Explanation:

Step1: Recall SI unit prefixes and conversions

We know the following conversions:

• \(1\space mm = 10^{-3}\space m\)
• \(1\space nm = 10^{-9}\space m\)
• \(1\space hm = 10^{2}\space m\)
• \(1\space cm = 10^{-2}\space m\)
• \(1\space Gm = 10^{9}\space m\)
• \(1\space dm = 10^{-1}\space m\)

Step2: Convert each measure to meters (m) in scientific notation

A: \(0.00000024\space mm\)

\(0.00000024\space mm = 0.00000024\times10^{-3}\space m = 2.4\times10^{-7}\times10^{-3}\space m = 2.4\times10^{-10}\space m\)

B: \(20\space nm\)

\(20\space nm = 20\times10^{-9}\space m = 2\times10^{1}\times10^{-9}\space m = 2\times10^{-8}\space m\)

C: \(9.3\times10^{1}\space m\)

This is already in meters: \(9.3\times10^{1}\space m = 93\space m\)

D: \(2\times10^{-6}\space hm\)

\(2\times10^{-6}\space hm = 2\times10^{-6}\times10^{2}\space m = 2\times10^{-4}\space m\)

E: \(40000000000\space cm\)

\(40000000000\space cm = 40000000000\times10^{-2}\space m = 4\times10^{10}\times10^{-2}\space m = 4\times10^{8}\space m\)

F: \(0.3\space Gm\)

\(0.3\space Gm = 0.3\times10^{9}\space m = 3\times10^{-1}\times10^{9}\space m = 3\times10^{8}\space m\)

G: Cent mille décimètres (100000 dm)

\(100000\space dm = 100000\times10^{-1}\space m = 1\times10^{5}\times10^{-1}\space m = 1\times10^{4}\space m\)

Step3: Order the measures in increasing order

Now we have the measures in meters:

• A: \(2.4\times10^{-10}\space m\)
• B: \(2\times10^{-8}\space m\)
• D: \(2\times10^{-4}\space m\)
• G: \(1\times10^{4}\space m\)
• C: \(9.3\times10^{1}\space m = 9.3\times10^{1}\space m\) (Wait, correction: \(9.3\times10^{1}=93\), \(1\times10^{4}=10000\), so order between C and G: \(93 < 10000\), so C comes before G)

Wait, re - ordering:

1. \(2.4\times10^{-10}\space m\) (A)
2. \(2\times10^{-8}\space m\) (B)
3. \(2\times10^{-4}\space m\) (D)
4. \(9.3\times10^{1}\space m\) (C)
5. \(1\times10^{4}\space m\) (G)
6. \(3\times10^{8}\space m\) (F)
7. \(4\times10^{8}\space m\) (E)

Answer:

The measures in increasing order (in meters) are:
A: \(2.4\times10^{-10}\space m\), B: \(2\times10^{-8}\space m\), D: \(2\times10^{-4}\space m\), C: \(9.3\times10^{1}\space m\), G: \(1\times10^{4}\space m\), F: \(3\times10^{8}\space m\), E: \(4\times10^{8}\space m\)

So the order of the original measures (A, B, C, D, E, F, G) in increasing order is: A, B, D, C, G, F, E