Civil Service Exam (Professional) Numerical Ability — Decimals & Scientific NotationFlash Cards

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When adding or subtracting decimals: 1) Align the decimal points vertically, 2) Add zeros to the right if needed to make equal decimal places, 3) Add or subtract as with whole numbers, 4) Place the decimal point in the answer directly below the aligned decimal points. Example: 12.5 + 0.35 = 12.50 + 0.35 = 12.85

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To multiply decimals: 1) Multiply as if they were whole numbers (ignore decimal points), 2) Count total decimal places in both factors, 3) Place decimal point in the product by moving left the same number of places. Example: 0.25 × 0.5 = 25 × 5 = 125, then place decimal 3 places from right = 0.125 (2 + 1 decimal places)

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To divide decimals: 1) Set up long division with dividend inside and divisor outside, 2) Move decimal point in divisor to the right to make it a whole number, 3) Move decimal point in dividend the same number of places, 4) Place decimal point in quotient directly above the new decimal point in dividend, 5) Divide as with whole numbers. Example: 0.4595 ÷ 0.05 becomes 45.95 ÷ 5 = 9.19

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To convert a percentage to a decimal, move the decimal point two places to the left (or divide by 100). Examples: 25% = 0.25, 30% = 0.30, 1.25% = 0.0125. Remember that percent means 'per hundred', so you're dividing by 100.

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The PRB triangle shows: P (Percentage) at top, R (Rate) and B (Base) at bottom. Formulas: P = R × B, R = P/B, B = P/R. To use: cover what you're solving for, and the remaining shows the operation. P is associated with 'is', R with '%' or 'percent', B with 'of'.

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Using P = R × B: P = 0.25 × 600 = 150. Always convert percentage to decimal first (25% = 0.25). This is a percentage problem where you're given the rate (25%) and base (600), solving for percentage.

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Using R = P/B: R = 400/2000 = 0.2 = 20%. This is a rate problem where you're given the percentage (400) and base (2000), solving for the rate. Convert the decimal result to percentage by multiplying by 100 or moving decimal point two places right.

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Using B = P/R: B = 210/0.30 = 700. This is a base problem where you're given the percentage (210) and rate (30%), solving for the base. Remember to convert percentage to decimal (30% = 0.30) before dividing.

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Method 1: 1/4 × 500 = 500/4 = 125. Method 2: Convert to percentage: 1/4 = 25%, so 0.25 × 500 = 125. Both methods give the same result. Fractions can be converted to percentages or used directly in multiplication.

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For fractions in percentage problems: 1) Convert mixed fractions to improper fractions, 2) Use the same PRB formulas (P = R × B, etc.), 3) When dividing fractions, multiply by the reciprocal, 4) Reduce final answers to lowest terms. Example: 1/2 is 3/4 of what number? → 1/2 ÷ 3/4 = 1/2 × 4/3 = 2/3

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A ratio is a comparison of two quantities of the same unit. It can be written in three ways: 1) Word form ('3 is to 1000'), 2) Fraction form (3/1000), 3) Colon form (3:1000). Example: ratio of 3 cm to 1000 cm can be written as 3:1000, 3/1000, or '3 is to 1000'.

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Ratio compares two quantities of the SAME unit (3 cm to 1000 cm). Rate compares two quantities of DIFFERENT units (3 km/hr, 3 pesos/orange). Both use division, but rate always involves different units of measurement.

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A proportion is a statement that two ratios are equal (a:b = c:d). To solve: the product of extremes equals the product of means (a × d = b × c). Example: 3:x = 1:5 → 3 × 5 = x × 1 → x = 15. Cross multiply to find the missing term.

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176.304 is read as 'one hundred seventy-six and three hundred four thousandths'. The whole number part (176) is read normally, 'and' represents the decimal point, and the decimal part (304) is read with its place value (thousandths, since it has 3 decimal places).

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To round 67.678 to the nearest hundredth: Look at the thousandths place (8). Since 8 ≥ 5, round up by adding 1 to the hundredths place (7 becomes 8) and drop the digits after. Result: 67.68 (Note: some texts show 67.680 to emphasize the place value).

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When multiplying by 10^n, move the decimal point n places to the RIGHT. Examples: 0.00095 × 1000 = 0.00095 × 10³ → move 3 places right = 0.95. When dividing by 10^n, move decimal point n places to the LEFT. Example: 69 ÷ 0.001 = 69 ÷ 10⁻³ = 69 × 10³ = 69,000.

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Direct proportion: As one variable increases, the other increases proportionally (ratio stays constant). Example: speed and distance with constant time. Inverse proportion: As one variable increases, the other decreases proportionally (product stays constant). Example: speed and time with constant distance.

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Method 1: Get equivalent fraction with denominator 100. Example: 1/4 = 25/100 = 25%. Method 2: Divide and multiply by 100. Example: 3/8 = 0.375 × 100% = 37.5%. Use Method 1 for simple fractions, Method 2 for complex ones.

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Calculate each product: 0.16 × 0.4 = 0.064, 0.17 × 0.5 = 0.085, 0.18 × 0.6 = 0.108. Add: 0.064 + 0.085 + 0.108 = 0.257. Remember to align decimal points when adding and count decimal places when multiplying.

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Amount spent: 15,000 × 0.25 = ₱3,750. Amount left: 15,000 - 3,750 = ₱11,250. Alternative: She has 75% left, so 15,000 × 0.75 = ₱11,250. Word problems require identifying what percentage represents and what operation to use.