Question

bellringer: week 9
nb pg. 34
answer the bellringer in complete sentences.

1. convert 0.00036 to scientific notation.
2. round 234,567 to 2 significant figures.
3. add: 12.11 + 0.034 + 0.2 → round to correct decimal place.
4. a light - year is 9,460,000,000,000 km. round to 3 significant figures and express in scientific notation.

Explanation:

Step1: Convert to scientific - notation for 0.00036

Move the decimal point 4 places to the right to get a number between 1 and 10. So, $0.00036 = 3.6\times10^{-4}$.

Step2: Round 234,567 to 2 significant figures

The first two significant figures are 2 and 3. Looking at the third digit (4), since it is less than 5, we round down. So, $234,567\approx2.3\times 10^{5}$.

Step3: Add 12.11 + 0.034 + 0.2

$12.11+0.034 + 0.2=12.344$. Rounding to the correct decimal place (hundredths place as 12.11 is the number with the least - precise decimal place among the addends), we get 12.34.

Step4: Round 9,460,000,000,000 to 3 significant figures and convert to scientific notation

The first three significant figures are 9, 4, and 6. Since the fourth digit is 0 (less than 5), we round down. So, $9,460,000,000,000\approx9.46\times 10^{12}$.

Answer:

1. $3.6\times10^{-4}$
2. $2.3\times 10^{5}$
3. 12.34
4. $9.46\times 10^{12}$