Decimals (operations, approximation, significant figures) — KCSE Mathematics

Rounding numbers is essential for simplifying calculations and reporting results. To round off a number:

1. Identify the digit at the specified decimal place.
2. Look at the next digit to the right:
   • If it is 5 or greater, increase the identified digit by 1.
   • If it is less than 5, keep the identified digit the same.

Significant figures are the digits that carry meaning contributing to its precision. To round to significant figures:

• Count from the first non-zero digit.
• Follow the same rounding rules as above.

Estimating answers involves simplifying numbers to make calculations easier. For example, use 3.14 as 3 for quick mental math.

Example: Round 7.456 to 2 decimal places. The digit in the second decimal place is 5, and the next digit is 6, so:

• 7.456 rounds to 7.46.

Example: Round 0.00456 to 2 significant figures. The first two significant figures are 4 and 5:

• Therefore, 0.00456 rounds to 0.0046.

Decimals are crucial in various contexts, including measurement, science, and everyday life. To apply decimal operations effectively, follow these steps:

1. Addition and Subtraction: Align decimal points before performing operations. For example, to add 2.75 and 3.6:

   • Align:
     2.75
   • 3.60
   • Result: 6.35

2. Multiplication: Multiply as whole numbers, then count total decimal places. For instance, multiplying 0.5 by 0.2:

   • 5 × 2 = 10 (2 decimal places total)
   • Result: 0.10 or 0.1

3. Division: Move the decimal point in the divisor to make it a whole number, then adjust the dividend accordingly. For example, dividing 2.5 by 0.5:

   • Move 0.5 to 5 (1 decimal place)
   • Adjust 2.5 to 25
   • Result: 25 ÷ 5 = 5

4. Rounding: Round decimals to the required significant figures for clarity in reporting results.

Decimals are crucial in mathematics for representing fractions and performing calculations. When dealing with decimals, it's important to understand the following operations:

• Addition/Subtraction: Align the decimal points before performing the operation. For example, to add 2.5 and 3.75:

  2.50

  • 3.75

  ---

  6.25

• Multiplication: Multiply as whole numbers and then count the total decimal places in both factors to place the decimal in the answer. For example, multiplying 2.5 by 0.4:

  25 x 4

  ---

  100

  The answer is 1.00 (or simply 1).

• Division: Move the decimal point in the divisor to make it a whole number, and do the same in the dividend. For example, dividing 3.6 by 0.9:

  3.6 ÷ 0.9 = 36 ÷ 9 = 4

Significant Figures: This refers to the digits that carry meaning contributing to its precision. For example, in the number 0.00456, there are three significant figures (456). Always round off to maintain the correct number of significant figures in your final answer.