High School

A. Convert the following decimals into fractions.
1. 0.6
2. 0.85
3. 0.45
4. 51.3

B. Convert the following fractions into decimals.
1. 10/25
2. 15/20
3. 6/5
4. 2/125

C. Express the following as fractions in the lowest form.
1. 0.75
2. 0.20
3. 0.150
4. 0.055

D. Fill in the boxes with <, > or = .
1. 7.05 7.50
2. 1.7 1 7/10
3. 5.85 5.058
4. 12.001 12.10
5. 8.12 8.63
6. 10.8 99.9
7. 0.4 0.5
8. 16.3 1.63
9. 1 1/2 1.5

Answer :

A. Converting decimals to fractions:

  1. [tex]0.6[/tex] can be written as [tex]\frac{6}{10}[/tex], which simplifies to [tex]\frac{3}{5}[/tex].

  2. [tex]0.85[/tex] can be written as [tex]\frac{85}{100}[/tex], which simplifies to [tex]\frac{17}{20}[/tex].

  3. [tex]0.45[/tex] can be written as [tex]\frac{45}{100}[/tex], which simplifies to [tex]\frac{9}{20}[/tex].

  4. [tex]51.3[/tex] can be expressed as [tex]51 + \frac{3}{10} = \frac{513}{10}[/tex].

B. Converting fractions to decimals:

  1. [tex]\frac{10}{25} = 0.4[/tex].

  2. [tex]\frac{15}{20} = 0.75[/tex].

  3. [tex]\frac{6}{5} = 1.2[/tex].

  4. [tex]\frac{2}{125} = 0.016[/tex].

C. Expressing decimals as fractions in lowest form:

  1. [tex]0.75[/tex] is [tex]\frac{75}{100}[/tex], which simplifies to [tex]\frac{3}{4}[/tex].

  2. [tex]0.20[/tex] is [tex]\frac{20}{100}[/tex], which simplifies to [tex]\frac{1}{5}[/tex].

  3. [tex]0.150[/tex] is [tex]\frac{150}{1000}[/tex], which simplifies to [tex]\frac{3}{20}[/tex].

  4. [tex]0.055[/tex] is [tex]\frac{55}{1000}[/tex], which simplifies to [tex]\frac{11}{200}[/tex].

D. Comparing numbers using <, >, or =:

  1. [tex]7.05 < 7.50[/tex]

  2. [tex]1.7 > 1 \frac{7}{10} (1.7)[/tex]

  3. [tex]5.85 > 5.058[/tex]

  4. [tex]12.00 < 12.10[/tex]

  5. [tex]8.12 < 8.63[/tex]

  6. [tex]10.8 < 99.9[/tex]

  7. [tex]0.4 < 0.58[/tex]

  8. [tex]16.3 > 1.63[/tex]

  9. [tex]1 \frac{1}{2} = 1.5[/tex]

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