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GRADE 10 PRACTICE

Physics Problems: SI and magnitude scales, Grade 10

Units, conversions and prefixes.

12 problems across 2 sub-topics
Practise in the interactive mode

Here the conditions and analysis of the solution can be read without an account. In the simulator, you need to collect the same analyzes yourself: “Given,” formulas, order of steps and answer.

Problem statements

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12 problems
Position in this set: 1 from 12

Problem #117

SI units and unit conversions

Wire length 250 cm. Express it in meters.

Answer options

  1. 2{,}5\,\text{м}
  2. 5\,\text{м}
  3. 1{,}25\,\text{м}
  4. 7{,}5\,\text{м}
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Given
l
250\,\text{см}
Find

x

  1. x=\frac{l}{100}x=\frac{250}{100}x=2{,}5\,\text{м}

    The prefix centi means one hundredth.

Answer2{,}5\,\text{м}

Position in this set: 2 from 12

Problem #118

SI units and unit conversions

Wire length 480 cm. Express it in meters.

Answer options

  1. 9{,}6\,\text{м}
  2. 4{,}8\,\text{м}
  3. 2{,}4\,\text{м}
  4. 14{,}4\,\text{м}
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Given
l
480\,\text{см}
Find

x

  1. x=\frac{l}{100}x=\frac{480}{100}x=4{,}8\,\text{м}

    The prefix centi means one hundredth.

Answer4{,}8\,\text{м}

Position in this set: 3 from 12

Problem #119

SI units and unit conversions

A rectangular plate has sides 20 cm and 30 cm. Find the area in m².

Answer options

  1. 0{,}12\,\text{м}^{2}
  2. 0{,}06\,\text{м}^{2}
  3. 0{,}03\,\text{м}^{2}
  4. 0{,}18\,\text{м}^{2}
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Given
a
20\,\text{см}
b
30\,\text{см}
Find

A

  1. S=abS=20 \cdot 30S=600\,\text{см}^{2}

    First, we calculate the area in the original units.

  2. A=\frac{S}{10^4}A=\frac{600}{10000}A=0{,}06\,\text{м}^{2}

    The length conversion factor is squared.

Answer0{,}06\,\text{м}^{2}

Position in this set: 4 from 12

Problem #120

SI units and unit conversions

A rectangular plate has sides 30 cm and 40 cm. Find the area in m².

Answer options

  1. 0{,}24\,\text{м}^{2}
  2. 0{,}06\,\text{м}^{2}
  3. 0{,}12\,\text{м}^{2}
  4. 0{,}36\,\text{м}^{2}
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Given
a
30\,\text{см}
b
40\,\text{см}
Find

A

  1. S=abS=30 \cdot 40S=1200\,\text{см}^{2}

    First, we calculate the area in the original units.

  2. A=\frac{S}{10^4}A=\frac{1200}{10000}A=0{,}12\,\text{м}^{2}

    The length conversion factor is squared.

Answer0{,}12\,\text{м}^{2}

Position in this set: 5 from 12

Problem #121

SI units and unit conversions

Sample mass 54 g has volume 20 cm³. Find its density in kg/m³.

Answer options

  1. 5400\,\text{кг/м}^{3}
  2. 1350\,\text{кг/м}^{3}
  3. 2700\,\text{кг/м}^{3}
  4. 8100\,\text{кг/м}^{3}
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Given
m
54\,\text{г}
V
20\,\text{см}^{3}
Find

\rho

  1. M=\frac{m}{1000}M=\frac{54}{1000}M=0{,}054\,\text{кг}

    Convert the mass to kilograms.

  2. v=\frac{V}{10^6}v=\frac{20}{1000000}v=0{,}00002\,\text{м}^{3}

    The length conversion factor is cubed.

  3. \rho=\frac{M}{v}\rho=\frac{0{,}054}{0{,}00002}\rho=2700\,\text{кг/м}^{3}

    We use both quantities in SI.

Answer2700\,\text{кг/м}^{3}

Position in this set: 6 from 12

Problem #122

SI units and unit conversions

Sample mass 156 g has volume 20 cm³. Find its density in kg/m³.

Answer options

  1. 15600\,\text{кг/м}^{3}
  2. 3900\,\text{кг/м}^{3}
  3. 23400\,\text{кг/м}^{3}
  4. 7800\,\text{кг/м}^{3}
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Given
m
156\,\text{г}
V
20\,\text{см}^{3}
Find

\rho

  1. M=\frac{m}{1000}M=\frac{156}{1000}M=0{,}156\,\text{кг}

    Convert the mass to kilograms.

  2. v=\frac{V}{10^6}v=\frac{20}{1000000}v=0{,}00002\,\text{м}^{3}

    The length conversion factor is cubed.

  3. \rho=\frac{M}{v}\rho=\frac{0{,}156}{0{,}00002}\rho=7800\,\text{кг/м}^{3}

    We use both quantities in SI.

Answer7800\,\text{кг/м}^{3}

Position in this set: 7 from 12

Problem #123

Decimal prefixes

Wire length 250 cm. Express it in meters.

Answer options

  1. 5\,\text{м}
  2. 2{,}5\,\text{м}
  3. 1{,}25\,\text{м}
  4. 7{,}5\,\text{м}
Show the walkthroughHide the walkthrough
Given
l
250\,\text{см}
Find

x

  1. x=\frac{l}{100}x=\frac{250}{100}x=2{,}5\,\text{м}

    The prefix centi means one hundredth.

Answer2{,}5\,\text{м}

Position in this set: 8 from 12

Problem #124

Decimal prefixes

Wire length 480 cm. Express it in meters.

Answer options

  1. 9{,}6\,\text{м}
  2. 2{,}4\,\text{м}
  3. 4{,}8\,\text{м}
  4. 14{,}4\,\text{м}
Show the walkthroughHide the walkthrough
Given
l
480\,\text{см}
Find

x

  1. x=\frac{l}{100}x=\frac{480}{100}x=4{,}8\,\text{м}

    The prefix centi means one hundredth.

Answer4{,}8\,\text{м}

Position in this set: 9 from 12

Problem #125

Decimal prefixes

A rectangular plate has sides 20 cm and 30 cm. Find the area in m².

Answer options

  1. 0{,}12\,\text{м}^{2}
  2. 0{,}03\,\text{м}^{2}
  3. 0{,}06\,\text{м}^{2}
  4. 0{,}18\,\text{м}^{2}
Show the walkthroughHide the walkthrough
Given
a
20\,\text{см}
b
30\,\text{см}
Find

A

  1. S=abS=20 \cdot 30S=600\,\text{см}^{2}

    First, we calculate the area in the original units.

  2. A=\frac{S}{10^4}A=\frac{600}{10000}A=0{,}06\,\text{м}^{2}

    The length conversion factor is squared.

Answer0{,}06\,\text{м}^{2}

Position in this set: 10 from 12

Problem #126

Decimal prefixes

A rectangular plate has sides 30 cm and 40 cm. Find the area in m².

Answer options

  1. 0{,}24\,\text{м}^{2}
  2. 0{,}06\,\text{м}^{2}
  3. 0{,}36\,\text{м}^{2}
  4. 0{,}12\,\text{м}^{2}
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Given
a
30\,\text{см}
b
40\,\text{см}
Find

A

  1. S=abS=30 \cdot 40S=1200\,\text{см}^{2}

    First, we calculate the area in the original units.

  2. A=\frac{S}{10^4}A=\frac{1200}{10000}A=0{,}12\,\text{м}^{2}

    The length conversion factor is squared.

Answer0{,}12\,\text{м}^{2}

Position in this set: 11 from 12

Problem #127

Decimal prefixes

Sample mass 54 g has volume 20 cm³. Find its density in kg/m³.

Answer options

  1. 5400\,\text{кг/м}^{3}
  2. 1350\,\text{кг/м}^{3}
  3. 8100\,\text{кг/м}^{3}
  4. 2700\,\text{кг/м}^{3}
Show the walkthroughHide the walkthrough
Given
m
54\,\text{г}
V
20\,\text{см}^{3}
Find

\rho

  1. M=\frac{m}{1000}M=\frac{54}{1000}M=0{,}054\,\text{кг}

    Convert the mass to kilograms.

  2. v=\frac{V}{10^6}v=\frac{20}{1000000}v=0{,}00002\,\text{м}^{3}

    The length conversion factor is cubed.

  3. \rho=\frac{M}{v}\rho=\frac{0{,}054}{0{,}00002}\rho=2700\,\text{кг/м}^{3}

    We use both quantities in SI.

Answer2700\,\text{кг/м}^{3}

Position in this set: 12 from 12

Problem #128

Decimal prefixes

Sample mass 156 g has volume 20 cm³. Find its density in kg/m³.

Answer options

  1. 7800\,\text{кг/м}^{3}
  2. 15600\,\text{кг/м}^{3}
  3. 3900\,\text{кг/м}^{3}
  4. 23400\,\text{кг/м}^{3}
Show the walkthroughHide the walkthrough
Given
m
156\,\text{г}
V
20\,\text{см}^{3}
Find

\rho

  1. M=\frac{m}{1000}M=\frac{156}{1000}M=0{,}156\,\text{кг}

    Convert the mass to kilograms.

  2. v=\frac{V}{10^6}v=\frac{20}{1000000}v=0{,}00002\,\text{м}^{3}

    The length conversion factor is cubed.

  3. \rho=\frac{M}{v}\rho=\frac{0{,}156}{0{,}00002}\rho=7800\,\text{кг/м}^{3}

    We use both quantities in SI.

Answer7800\,\text{кг/м}^{3}

The theory behind these problems

Work through the topic if a problem will not give in.

SI units and unit conversionsBase units and conversions of length, area, volume, mass and time.Decimal prefixesPrefixes from pico to tera and calculations with powers of ten.

Formulas by topic

Look up symbols and units of measurement in the reference.

Timet, τ · сHeight and depthh · мWavelengthλ · мMassm · кгDistance and pathS, l · мElectric currentI · А