Home
Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes
Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation
Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
Sign InJoin

Logarithmic Scales - Magnitude Difference to Measured Value Ratio

Level 2

This math topic focuses on the relationship between magnitude differences and their corresponding measured value ratios when represented on logarithmic scales. Specifically, it involves calculating the ratios of measured values for changes in magnitudes on the Richter scale for earthquakes, and on the decibel scale for sound intensities. These types of problems are crucial in understanding how small changes in magnitude can correspond to exponential differences in real-world measurements. Each problem provides two answer choices, highlighting how logarithmic calculations can impact interpretation of data in scientific contexts.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

more
WorksheetView

Logarithmic Scales - Magnitude Difference to Measured Value Ratio Worksheet

Mobius Math Academy logo
Logarithmic Scales - Magnitude Difference to Measured Value Ratio
1
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 0.1
If an earthquake has a magnitude 0.1 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 39.8
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1.26
2
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 3.2
If an earthquake has a magnitude 3.2 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,585
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 15.8
3
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 2.1
If an earthquake has a magnitude 2.1 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 126
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 12,589
4
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 3.1
If an earthquake has a magnitude 3.1 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 1,259
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 39,811
5
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 3.7
If an earthquake has a magnitude 3.7 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 501
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 5,012
6
A LaTex expression showing \text{M} = \log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \text{M} sub 2 - \text{M} sub 1 = 7.3
If an earthquake has a magnitude 7.3 higher on the Richter scale what is the ratio of their wave size measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 2 multiplied by 10 to the power of 8
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 2 multiplied by 10 to the power of 7
7
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 46
If a sound has a dB magnitude 46 higher on the decibel scale what is the ratio of their sound energy measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 158,489
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 39,811
8
A LaTex expression showing \text{dB} = 10\log{(\frac{\text{I}}{\text{I} sub 0 })}\\ \\ \beta sub 2 - \beta sub 1 = 27
If a sound has a dB magnitude 27 higher on the decibel scale what is the ratio of their sound energy measurements?
a A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 501
b A LaTex expression showing \frac{\text{I} sub 2 }{\text{I} sub 1 } = 2,512