Simplify: 1.2x1.2x1.2-0.12x0.12x0.12/12x12x12

Appeared in: RRB Nsg. Superintendent-2026 (Shift -2nd)

Explanation

The expression can be simplified by rewriting the decimal numbers as multiples of 12.
2 can be written as (12 x 10⁻¹) and 0.12 as (12 x 10⁻²).
Substituting these values gives [(12³ x 10⁻³) - (12³ x 10⁻⁶)] / 12³.
Factoring out and cancelling the common term 12³ from the numerator and denominator leaves 10⁻³ - 10⁻⁶.
This simplifies to 0.001 - 0.000001, which equals 0.000999.

Option A: This value (0.0000999) would be obtained if the calculation was 10⁻⁴ - 10⁻⁷, indicating an error in handling the powers of ten.
Option B: This value (0.00999) would be obtained if the calculation was 10⁻² - 10⁻⁵, suggesting a misinterpretation of the decimal places in the original numbers.
Option C: This value (0.0999) would be obtained if the calculation was 10⁻¹ - 10⁻⁴, which would imply a significant misreading of the problem, possibly ignoring the exponents on the decimal terms.

Visual 1: Flowchart - A step-by-step flowchart illustrating the simplification process, from rewriting the decimals to factoring out common terms and performing the final subtraction.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Simplification of numerical expressions involving exponents and decimals as background academic context rather than a clinical decision trigger.
This question tests basic numeracy and analytical skills, which are fundamental for a nursing professional.
Accurate calculation is critical in nursing for tasks such as medication dosage calculation, IV drip rate regulation, and interpreting lab results.
What if? If the denominator was 1.2³ instead of 12³, the common term to cancel would be 1.2³, and the result would be 1 - (0.1)³, which is 1 - 0.001 = 0.999.

How to Approach the Question

First, analyze the expression to identify any patterns or common factors among the numbers.
Notice that 1.2 and 0.12 are related to 12 by powers of 10.
Rewrite the expression using this relationship: (1.2 = 12 x 10⁻¹) and (0.12 = 12 x 10⁻²).
Use the laws of exponents to simplify the numerator and factor out the common term (12³).
Cancel the common term from the numerator and denominator.
Perform the final subtraction of the remaining powers of 10 to get the answer.

Concept Tested & Keywords

Concept Tested: Simplification of numerical expressions involving exponents and decimals.
Stem keywords: Simplify, Decimals, Exponents, Fractions
Lead-in keywords: Simplify

QbDlJosnj4sQ0cmP7GFcet

Practise the full RRB Nsg. Superintendent-2026 (Shift -2nd)

Attempt every question from this paper in a timed mock, then review the full solution for each one.