Question

identify the lesser number, and justify your reasoning.
13 8.7×10^4 or 5.9×10^3
14 4.8×10^3 or 9.6×10^7
15 3.1×10^(-5) or 7.5×10^(-5)
16 6.9×10^(-3) or 4.3×10^(-3)
solve. show your work.
17 the table shows population data for four countries. write each population in scientific notation.
country population
brazil 210000000
singapore 5640000
monaco 38700
fiji 883000
19 a technician reads and records the air pressure from several pressure gauges. the table shows each air - pressure reading in pascals(pa). a pascal is a unit used to measure the amount of force applied on a given area by air or other gases.
pressure gauge air pressure (pa)
a 210000
b 5.2×10^5
c 170000

Explanation:

Step1: Compare numbers in scientific - notation

When comparing numbers in scientific notation $a\times10^{n}$, if the exponents $n$ are different, the number with the larger exponent is larger. If the exponents are the same, the number with the larger $a$ value is larger.

13.

For $8.7\times 10^{4}$ and $5.9\times 10^{3}$, since $4>3$, $5.9\times 10^{3}$ is the lesser number.

14.

For $4.8\times 10^{3}$ and $9.6\times 10^{7}$, since $7 > 3$, $4.8\times 10^{3}$ is the lesser number.

15.

For $3.1\times 10^{-5}$ and $7.5\times 10^{-5}$, the exponents are the same ($n=-5$). Since $3.1<7.5$, $3.1\times 10^{-5}$ is the lesser number.

16.

For $6.9\times 10^{-3}$ and $4.3\times 10^{-3}$, the exponents are the same ($n = - 3$). Since $4.3<6.9$, $4.3\times 10^{-3}$ is the lesser number.

17.

• Brazil: $210000000=2.1\times 10^{8}$
• Singapore: $5640000 = 5.64\times 10^{6}$
• Monaco: $38700=3.87\times 10^{4}$
• Fiji: $883000=8.83\times 10^{5}$

19.

• First, rewrite all values in scientific - notation:
• Gauge A: $210000 = 2.1\times 10^{5}$
• Gauge B: $5.2\times 10^{5}$
• Gauge C: $170000=1.7\times 10^{5}$
• Compare the numbers: Since $5.2>2.1>1.7$, gauge B has the greatest reading.
• Gauge C has the least reading as $1.7\times 10^{5}<2.1\times 10^{5}<5.2\times 10^{5}$.
• The atmospheric pressure is $1.1\times 10^{5}$ pascals. Gauge B ($5.2\times 10^{5}$) has a reading greater than the atmospheric pressure.

Answer:

1. Lesser number: $5.9\times 10^{3}$
2. Lesser number: $4.8\times 10^{3}$
3. Lesser number: $3.1\times 10^{-5}$
4. Lesser number: $4.3\times 10^{-3}$
5. Brazil: $2.1\times 10^{8}$, Singapore: $5.64\times 10^{6}$, Monaco: $3.87\times 10^{4}$, Fiji: $8.83\times 10^{5}$
6. a. Gauge B has the greatest reading.

b. Gauge C has the least reading.
c. Gauge B showed a reading greater than the atmospheric pressure.