Versalog 1460 Practice Solutions

How to Use These Solutions

Each solution explains the estimate, scale selection, slide and cursor movements, decimal placement and final interpretation. The objective is to understand the method rather than merely obtain an answer.

Basic Arithmetic Solutions

4 × 7

  • Estimate: 4 × 7 is close to 30.
  • Scales: use C and D.
  • Place the left C index over 4 on D.
  • Move the cursor to 7 on C.
  • Read 2.8 on D.
  • Decimal placement: the estimate shows that the result is 28, not 2.8 or 280.
  • Answer: 28.

12 × 3.5

  • Estimate: 12 × 3.5 is slightly more than 12 × 3, so expect a result near 40.
  • Scales: use C and D.
  • Treat 12 as 1.2 on D and place the appropriate C index over it.
  • Move the cursor to 3.5 on C.
  • Read approximately 4.2 on D.
  • Decimal placement: the estimate establishes the result as 42.
  • Answer: 42.

25 × 16

  • Estimate: 25 × 16 is four groups of 100, so expect approximately 400.
  • Scales: use C and D.
  • Represent 25 as 2.5 on D.
  • Align the appropriate C index and locate 1.6 on C.
  • Read approximately 4.0 on D.
  • Decimal placement: the estimate establishes the result as 400.
  • Answer: 400.

144 ÷ 12

  • Estimate: 144 divided by 12 should be slightly greater than 10.
  • Scales: use C and D.
  • Place 1.2 on C over 1.44 on D.
  • Move the cursor to the C index.
  • Read 1.2 on D.
  • Decimal placement: the estimate establishes the result as 12.
  • Answer: 12.

360 ÷ 45

  • Estimate: 360 ÷ 40 is 9, so expect a result slightly below 9.
  • Scales: use C and D.
  • Place 4.5 on C over 3.6 on D.
  • Move the cursor to the appropriate C index.
  • Read approximately 8.0 on D after applying the correct magnitude.
  • Answer: 8.

875 ÷ 25

  • Estimate: 900 ÷ 25 is 36, so expect a result near 35.
  • Scales: use C and D.
  • Place 2.5 on C over 8.75 on D.
  • Move the cursor to the appropriate C index.
  • Read approximately 3.5 on D.
  • Decimal placement: the estimate establishes the result as 35.
  • Answer: 35.

CI Scale Solutions

100 ÷ 4

  • Estimate: one quarter of 100 is 25.
  • Scale selection: CI represents reciprocal values, so 4 on CI corresponds to 1 ÷ 4.
  • Use the cursor to align 4 on CI with the required D-scale relationship.
  • Read the reciprocal factor as 2.5 on D.
  • Decimal placement: the estimate establishes the result as 25.
  • Answer: 25.

250 ÷ 5

  • Estimate: one fifth of 250 is 50.
  • Scale selection: use CI to introduce the reciprocal of 5.
  • Align the reciprocal relationship with 2.5 on D.
  • Read approximately 5.0 on D.
  • Decimal placement: the estimate establishes the result as 50.
  • Answer: 50.

1,200 ÷ 8

  • Estimate: 1,200 ÷ 10 is 120, so dividing by 8 should give a somewhat larger result.
  • Scale selection: use the reciprocal relationship on CI.
  • Apply the reciprocal of 8 to 1.2 on D.
  • Read approximately 1.5 on D.
  • Decimal placement: the estimate establishes the result as 150.
  • Answer: 150.

75 × 0.4

  • Estimate: 40 per cent of 75 is 30.
  • Scale selection: the calculation may be treated as 75 × 4 ÷ 10 and completed using C, D and CI relationships.
  • Represent 75 as 7.5 on D.
  • Apply the factor 4 while accounting for division by 10 through decimal placement.
  • Read approximately 3.0.
  • Answer: 30.

48 ÷ 1.5

  • Estimate: 48 ÷ 1.5 must be less than 48 but greater than 24.
  • Scale selection: use CI for the reciprocal of 1.5.
  • Apply the reciprocal relationship to 4.8 on D.
  • Read approximately 3.2 on D.
  • Decimal placement: the estimate establishes the result as 32.
  • Answer: 32.

Powers and Roots Solutions

6²

  • Estimate: 6² is between 5² and 10², so expect a result between 25 and 100.
  • Scales: use D and A.
  • Place the cursor over 6 on D.
  • Read 36 on A.
  • Answer: 36.

12²

  • Estimate: 12² is slightly greater than 10², so expect a result somewhat greater than 100.
  • Scales: use D and A.
  • Represent 12 as 1.2 on D.
  • Read 1.44 on A.
  • Decimal placement: the estimate establishes the result as 144.
  • Answer: 144.

√81

  • Estimate: the answer is between 8 and 10.
  • Scales: use A and D.
  • Locate 81 on the appropriate half of A.
  • Move the cursor to that position.
  • Read 9 on D.
  • Answer: 9.

√225

  • Estimate: 15² is a familiar reference value near 225.
  • Scales: use A and D.
  • Locate 2.25 on the appropriate A-scale section.
  • Read 1.5 on D.
  • Decimal placement: the estimate establishes the result as 15.
  • Answer: 15.

4³

  • Estimate: 4 × 4 × 4 is somewhat greater than 50.
  • Scale: use K.
  • Locate 4 on the corresponding base scale and transfer the position with the cursor.
  • Read approximately 64 on K.
  • Answer: 64.

∛125

  • Estimate: 5³ is a familiar reference value.
  • Scale: use K in reverse.
  • Locate 125 on the appropriate K-scale section.
  • Transfer the position with the cursor.
  • Read 5 on the corresponding base scale.
  • Answer: 5.

Folded Scale Solutions

Circumference of a Circle with Radius 25 mm

The formula is circumference = 2πr.

  • Estimate: 2 × 3 × 25 is approximately 150 mm.
  • Scales: CF and DF are useful because they incorporate the π relationship efficiently.
  • Apply the factor 2π to 25 mm using the folded-scale relationship.
  • Read approximately 1.57.
  • Decimal placement and units: the estimate establishes 157 mm.
  • Answer: approximately 157 mm.

Area of a Circle with Radius 40 mm

The formula is area = πr².

  • Estimate: 40² = 1,600 and multiplying by slightly more than 3 gives slightly more than 4,800 mm².
  • Use A or D/A to obtain 40².
  • Use CF and DF, or C and D, to multiply by π.
  • Read approximately 5.03.
  • Decimal placement and units: the result is approximately 5,030 mm².
  • Answer: approximately 5,027 mm² to calculator precision; report only the precision supported by the slide-rule reading.

Cylinder Volume

The original exercise does not specify a radius or height, so it has no single numerical answer.

  • Use the formula volume = πr²h.
  • Square the radius using A and D.
  • Multiply by π using CF and DF or C and D.
  • Multiply by the height.
  • Express the result in cubic units.

Trigonometric Solutions

  • sin 30°: locate 30° on S and read approximately 0.5 on the corresponding reference scale.
  • sin 45°: locate 45° on S and read approximately 0.707.
  • tan 45°: locate 45° on T and read approximately 1.0.
  • tan 60°: locate 60° on T and read approximately 1.73.

The right-triangle exercise has no specified side lengths or angle, so it does not have a single numerical answer. Select S for sine relationships or T for tangent relationships according to the known and unknown quantities.

Logarithmic Solutions

  • log₁₀(10) = 1.
  • log₁₀(100) = 2.

The fractional-power and exponential exercises do not specify base values or exponents, so they do not have numerical answers. Use the appropriate LL range after identifying the base and exponent, then verify whether the result should increase or decrease.

Engineering Practice Guidance

The engineering exercises describe calculation types but do not provide numerical input values. Their purpose is to practise method selection.

  • For multiplication, division and a square root, complete the product and quotient efficiently, then transfer the result between A and D to obtain the square root.
  • For π and a squared dimension, square the dimension first and then use the folded scales for the π factor.
  • For an exponential term, select the appropriate LL scale range.
  • For trigonometry followed by multiplication, obtain the trigonometric ratio first and retain it with the cursor before applying the remaining factor.

Final Check

For every solution, confirm the scale selection, direction of movement, decimal placement, units and expected order of magnitude. A slide-rule answer is not complete until those checks have been made.

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